We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism, and determine precisely when the invariant ring for the coaction is Artin-Schelter regular. The proofs of our results are combinatorial and exploit the structure of the McKay quiver associated to the coaction.
{"title":"Group coactions on two-dimensional Artin-Schelter regular algebras","authors":"Simon Crawford","doi":"10.1090/proc/16844","DOIUrl":"https://doi.org/10.1090/proc/16844","url":null,"abstract":"<p>We describe all possible coactions of finite groups (equivalently, all group gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary and sufficient conditions for the associated Auslander map to be an isomorphism, and determine precisely when the invariant ring for the coaction is Artin-Schelter regular. The proofs of our results are combinatorial and exploit the structure of the McKay quiver associated to the coaction.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"4 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Retraction notice","authors":"Khadime Salame","doi":"10.1090/proc/16856","DOIUrl":"https://doi.org/10.1090/proc/16856","url":null,"abstract":"","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"61 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we show that the pp-adic limit of a family of Eisenstein series on the exceptional domain where the exceptional group of type E7,3E_{7,3} acts is an ordinary modular form for a congruence subgroup.
在本文中，我们证明了在类型为 E 7 , 3 E_{7,3} 的卓越群作用的卓越域上，爱森斯坦级数族的 p p -adic 极限是一个全等子群的普通模态。
{"title":"𝑝-adic limit of the Eisenstein series on the exceptional group of type 𝐸_{7,3}","authors":"Hidenori Katsurada, Henry Kim","doi":"10.1090/proc/16866","DOIUrl":"https://doi.org/10.1090/proc/16866","url":null,"abstract":"<p>In this paper, we show that the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic limit of a family of Eisenstein series on the exceptional domain where the exceptional group of type <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E Subscript 7 comma 3\"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mn>7</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding=\"application/x-tex\">E_{7,3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> acts is an ordinary modular form for a congruence subgroup.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"26 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main purpose of this short note is to derive some generalizations of the long neck principle and give a spectral width inequality of geodesic collar neighborhoods. Our results are obtained via the spinorial Callias operator approach. An important step is to introduce the relative Gromov-Lawson pair on a compact manifold with boundary, relative to a background manifold.
{"title":"A note on the long neck principle and spectral width inequality of geodesic collar neighborhoods","authors":"Daoqiang Liu","doi":"10.1090/proc/16869","DOIUrl":"https://doi.org/10.1090/proc/16869","url":null,"abstract":"<p>The main purpose of this short note is to derive some generalizations of the long neck principle and give a spectral width inequality of geodesic collar neighborhoods. Our results are obtained via the spinorial Callias operator approach. An important step is to introduce the relative Gromov-Lawson pair on a compact manifold with boundary, relative to a background manifold.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"8 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we construct a bounded wandering domain with the property that, in a sense we make precise, nearly all of its forward iterates are contained within a bounded domain.
{"title":"Wandering domains with nearly bounded orbits","authors":"Leticia Pardo-Simón, David Sixsmith","doi":"10.1090/proc/16846","DOIUrl":"https://doi.org/10.1090/proc/16846","url":null,"abstract":"<p>In this paper we construct a bounded wandering domain with the property that, in a sense we make precise, nearly all of its forward iterates are contained within a bounded domain.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let ΣHk(p)Sigma _H^k(p) be the class of sense-preserving univalent harmonic mappings defined on the open unit disk Dmathbb {D} of the complex plane with a simple pole at z=p∈(0,1)z=p in (0,1) that have kk-quasiconformal extensions (0≤k>10leq k>1) onto the extended complex plane. In this article, we obtain an area theorem for this class of functions.
设 Σ H k ( p ) Sigma _H^k(p)是一类定义在复平面的开放单位盘 D mathbb {D} 上、在 z = p∈ ( 0 , 1 ) z=p (0,1)处有一个简单极点、在扩展复平面上有 k k -等方扩展（0 ≤ k > 1 0leq k>1 ）的保感单等调和映射。在本文中，我们得到了这一类函数的面积定理。
{"title":"An area theorem for harmonic mappings with nonzero pole having quasiconformal extensions","authors":"Bappaditya Bhowmik, Goutam Satpati","doi":"10.1090/proc/16850","DOIUrl":"https://doi.org/10.1090/proc/16850","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Sigma Subscript upper H Superscript k Baseline left-parenthesis p right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi mathvariant=\"normal\">Σ</mml:mi> <mml:mi>H</mml:mi> <mml:mi>k</mml:mi> </mml:msubsup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Sigma _H^k(p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the class of sense-preserving univalent harmonic mappings defined on the open unit disk <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper D\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"double-struck\">D</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbb {D}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the complex plane with a simple pole at <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"z equals p element-of left-parenthesis 0 comma 1 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mi>p</mml:mi> <mml:mo>∈</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">z=p in (0,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that have <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-quasiconformal extensions (<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0 less-than-or-equal-to k greater-than 1\"> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>k</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">0leq k>1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) onto the extended complex plane. In this article, we obtain an area theorem for this class of functions.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"53 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let ΓGamma be a finitely generated group which admits an action by homeomorphisms on a metrizable space XX. We show that there is a metric on XX defining the original topology such that for this metric, the action is by bi-Lipschitz transformations.
让 Γ Gamma 是一个有限生成的群，它在可元空间 X X 上允许同构作用。我们将证明在 X X 上存在一个定义了原始拓扑的度量，对于这个度量，作用是通过双利普西茨变换实现的。
{"title":"Actions of finitely generated groups on compact metric spaces","authors":"Ursula Hamenstädt","doi":"10.1090/proc/16865","DOIUrl":"https://doi.org/10.1090/proc/16865","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Gamma\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Γ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a finitely generated group which admits an action by homeomorphisms on a metrizable space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that there is a metric on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> defining the original topology such that for this metric, the action is by bi-Lipschitz transformations.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"34 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we are concerned with the computations of the pp-rank of curves in two different setups. We first work with complete intersection varieties in Pn for n≥2mathbf {P}^n text { for } nge 2 and compute explicitly the action of Frobenius on the top cohomology group. In case of curves and surfaces, this information suffices to determine if the variety is ordinary. Next, we consider curves on more general surfaces with pg(S)=0=q(S)p_g(S) = 0 = q(S) such as Hirzebruch surfaces and determine pp-rank of curves on Hirzebruch surfaces.
在本文中，我们关注两种不同情况下曲线 p p -rank 的计算。我们首先处理 n ≥ 2 mathbf {P}^n text { for } nge 2 的 P n 中的完全交集品种，并明确计算 Frobenius 对顶同调群的作用。在曲线和曲面的情况下，这些信息足以确定该变化是否普通。接下来，我们考虑更一般的曲面上的曲线，即 p g ( S ) = 0 = q ( S ) p_g(S) = 0 = q(S)，如希尔泽布鲁赫曲面，并确定希尔泽布鲁赫曲面上曲线的 p p -rank。
{"title":"On the 𝑝-rank of curves","authors":"Sadik Terzİ","doi":"10.1090/proc/16841","DOIUrl":"https://doi.org/10.1090/proc/16841","url":null,"abstract":"<p>In this paper, we are concerned with the computations of the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-rank of curves in two different setups. We first work with complete intersection varieties in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"bold upper P Superscript n Baseline for n greater-than-or-equal-to 2\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"bold\">P</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mtext> for </mml:mtext> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbf {P}^n text { for } nge 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and compute explicitly the action of Frobenius on the top cohomology group. In case of curves and surfaces, this information suffices to determine if the variety is ordinary. Next, we consider curves on more general surfaces with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p Subscript g Baseline left-parenthesis upper S right-parenthesis equals 0 equals q left-parenthesis upper S right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>S</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>=</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>S</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">p_g(S) = 0 = q(S)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such as Hirzebruch surfaces and determine <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-rank of curves on Hirzebruch surfaces.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"54 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<p>In the present paper, we study the shifted hypergeometric function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis z right-parenthesis equals z 2 upper F 1 left-parenthesis a comma b semicolon c semicolon z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>z</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>;</mml:mo> <mml:mi>c</mml:mi> <mml:mo>;</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">f(z)=z_{2}F_{1}(a,b;c;z)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for real parameters with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0 greater-than a less-than-or-equal-to b less-than-or-equal-to c"> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>></mml:mo> <mml:mi>a</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>b</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">0>ale ble c</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and its variant <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g left-parenthesis z right-parenthesis equals z 2 upper F 2 left-parenthesis a comma b semicolon c semicolon z squared right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>z</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>;</mml:mo> <mml:mi>c</mml:mi> <mml:mo>;</mml:mo> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">g(z)=z_{2}F_{2}(a,b;c;z^2)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Our first purpose is to solve the range problems for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding="application/x-tex">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding="application/x-tex">g</mml:annotation
本文研究了实参数为 0 > a ≤ b ≤ c 0>ale ble c 时的移位超几何函数 f ( z ) = z 2 F 1 ( a , b ; c ; z ) f(z)=z_{2}F_{1}(a,b;c.) f(z)=z_{2}F_{1}(a,b;c.)和它的变体 g ( z ) = z 2 F 2 ( a , b ; c ; z 2 ) g(z)=z_{2}F_{2}(a,b;c;z^2) 。我们的第一个目的是解决 Ponnusamy 和 Vuorinen [Rocky Mountain J. Math. 31 (2001)，pp.］Ruscheweyh, Salinas and Sugawa [Israel J. Math. 171 (2009), pp. mathbb {C}setminus [1,+infty ) 并在参数的一些假设下证明了 f f 的普遍星象性。然而，除了 b = 1 b=1 的情况之外，还没有系统地研究过移位超几何函数的普遍凸性。我们的第二个目的是在参数的某些条件下证明 f f 的普遍凸性。
{"title":"Universal convexity and range problems of shifted hypergeometric functions","authors":"Toshiyuki Sugawa, Li-Mei Wang, Chengfa Wu","doi":"10.1090/proc/16849","DOIUrl":"https://doi.org/10.1090/proc/16849","url":null,"abstract":"<p>In the present paper, we study the shifted hypergeometric function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f left-parenthesis z right-parenthesis equals z 2 upper F 1 left-parenthesis a comma b semicolon c semicolon z right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>z</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>;</mml:mo> <mml:mi>c</mml:mi> <mml:mo>;</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">f(z)=z_{2}F_{1}(a,b;c;z)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for real parameters with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0 greater-than a less-than-or-equal-to b less-than-or-equal-to c\"> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>></mml:mo> <mml:mi>a</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>b</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">0>ale ble c</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and its variant <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g left-parenthesis z right-parenthesis equals z 2 upper F 2 left-parenthesis a comma b semicolon c semicolon z squared right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>z</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>;</mml:mo> <mml:mi>c</mml:mi> <mml:mo>;</mml:mo> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">g(z)=z_{2}F_{2}(a,b;c;z^2)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Our first purpose is to solve the range problems for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=\"application/x-tex\">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=\"application/x-tex\">g</mml:annotation","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"12 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<p>Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V"> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding="application/x-tex">V</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a vertex algebra of countable dimension, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a subgroup of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A u t upper V"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>u</mml:mi> <mml:mi>t</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">AutV</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of finite order, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V Superscript upper G"> <mml:semantics> <mml:msup> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">V^{G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the fixed point subalgebra of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V"> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding="application/x-tex">V</mml:annotation> </mml:semantics> </mml:math> </inline-formula> under the action of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper S"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">S</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">mathscr {S}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a finite <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-stable set of inequivalent irreducible twisted weak <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V"> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding="application/x-tex">V</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules associated with possibly different automorphisms in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" al
让 V V 是一个可数维度的顶点代数，G G 是 A u t V AutV 的一个有限阶的子群，V G V^{G} 是 V V 在 G G 作用下的定点子代数，而 S mathscr {S} 是一个有限的 G G 稳定集合，由与 G G 中可能不同的自变量相关联的不等价的不可还原的扭曲弱 V V 模块组成。我们展示了 A α ( G , S ) mathscr {A}_{alpha }(G,mathscr {S}) 和 V G V^G 对 S mathscr {S} 中扭曲弱 V V 模量的直接和的作用的舒尔-韦尔型对偶性，其中 A α ( G 、 S ) 是与 G , S G , mathscr {S} 相关联的有限维半简单关联代数，以及由 G G 在 S mathscr {S} 上的作用自然决定的 2 2 -环 α alpha 。结果的一个自然结果是，对于任意 g ∈ G gin G，每一个不可还原的 g g -扭曲弱 V V -模块都是一个完全可还原的弱 V G V^G -模块。
{"title":"A Schur-Weyl type duality for twisted weak modules over a vertex algebra","authors":"Kenichiro Tanabe","doi":"10.1090/proc/16843","DOIUrl":"https://doi.org/10.1090/proc/16843","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\"> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding=\"application/x-tex\">V</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a vertex algebra of countable dimension, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a subgroup of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A u t upper V\"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>u</mml:mi> <mml:mi>t</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">AutV</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of finite order, <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V Superscript upper G\"> <mml:semantics> <mml:msup> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">V^{G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the fixed point subalgebra of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\"> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding=\"application/x-tex\">V</mml:annotation> </mml:semantics> </mml:math> </inline-formula> under the action of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper S\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">S</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathscr {S}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a finite <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-stable set of inequivalent irreducible twisted weak <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\"> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding=\"application/x-tex\">V</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules associated with possibly different automorphisms in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" al","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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