Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108148
Marian Aprodu , Andrea Bruno , Edoardo Sernesi
The present paper is a natural continuation of the previous work [2] where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second syzygy scheme of a genus–g curve of degree at least coincides with the curve. If the property is satisfied, the equality is ensured by a more general fact emphasized in [2]. If fails, then the analysis uses the known case of canonical curves.
{"title":"The second syzygy schemes of curves of large degree","authors":"Marian Aprodu , Andrea Bruno , Edoardo Sernesi","doi":"10.1016/j.jpaa.2025.108148","DOIUrl":"10.1016/j.jpaa.2025.108148","url":null,"abstract":"<div><div>The present paper is a natural continuation of the previous work <span><span>[2]</span></span> where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second syzygy scheme of a genus–<em>g</em> curve of degree at least <span><math><mn>2</mn><mi>g</mi><mo>+</mo><mn>2</mn></math></span> coincides with the curve. If the property <span><math><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> is satisfied, the equality is ensured by a more general fact emphasized in <span><span>[2]</span></span>. If <span><math><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> fails, then the analysis uses the known case of canonical curves.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108148"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108157
Jiayi Chen , Bangming Deng , Shiquan Ruan
This paper deals with the triangle singularity defined by the equation for a weight triple , as well as the category of coherent sheaves over the weighted projective line defined by f. We calculate Hall polynomials associated with extension bundles, line bundles and torsion sheaves over . By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi (2024) [35].
{"title":"Hall polynomials for weighted projective lines","authors":"Jiayi Chen , Bangming Deng , Shiquan Ruan","doi":"10.1016/j.jpaa.2025.108157","DOIUrl":"10.1016/j.jpaa.2025.108157","url":null,"abstract":"<div><div>This paper deals with the triangle singularity defined by the equation <span><math><mi>f</mi><mo>=</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>3</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msubsup></math></span> for a weight triple <span><math><mo>(</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>, as well as the category of coherent sheaves over the weighted projective line <span><math><mi>X</mi></math></span> defined by <em>f</em>. We calculate Hall polynomials associated with extension bundles, line bundles and torsion sheaves over <span><math><mi>X</mi></math></span>. By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi (2024) <span><span>[35]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108157"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108151
Barbara Gatti , Gioia Schulte
In the study of algebraic curves with many points over a finite field, a well known general problem is to understand better the properties of -maximal curves whose genera fall in the higher part of the spectrum of the genera of all -maximal curves. This problem is still open for genera smaller than . In this paper we consider the case of where and the curve is the Galois subcover of the Hermitian curve w.r.t. a cyclic automorphism group of order 4. Our contributions concern Frobenius embedding, Weierstrass semigroups and automorphism groups.
{"title":"On a Galois subcover of the Hermitian curve of genus g=18(q−1)2","authors":"Barbara Gatti , Gioia Schulte","doi":"10.1016/j.jpaa.2025.108151","DOIUrl":"10.1016/j.jpaa.2025.108151","url":null,"abstract":"<div><div>In the study of algebraic curves with many points over a finite field, a well known general problem is to understand better the properties of <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span>-maximal curves whose genera fall in the higher part of the spectrum of the genera of all <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span>-maximal curves. This problem is still open for genera smaller than <span><math><mo>⌊</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>q</mi><mo>+</mo><mn>4</mn><mo>)</mo><mo>⌋</mo></math></span>. In this paper we consider the case of <span><math><mi>g</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>8</mn></mrow></mfrac><msup><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> where <span><math><mi>q</mi><mo>≡</mo><mn>1</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn><mo>)</mo></math></span> and the curve is the Galois subcover of the Hermitian curve w.r.t. a cyclic automorphism group of order 4. Our contributions concern Frobenius embedding, Weierstrass semigroups and automorphism groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108151"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108156
Emile Bouaziz
We write down an explicit operator on the chiral de Rham complex of a Calabi-Yau variety X which intertwines the usual module structure with its twist by the spectral flow automorphism of the , producing the expected spectral flow equivariance. Taking the trace of the operators and on cohomology, and using the obvious interaction of spectral flow with characters, we obtain an explicit categorification of ellipticity of the elliptic genus of X, which is well known by other means.
{"title":"Spectral flow equivariance for Calabi-Yau Sigma models","authors":"Emile Bouaziz","doi":"10.1016/j.jpaa.2025.108156","DOIUrl":"10.1016/j.jpaa.2025.108156","url":null,"abstract":"<div><div>We write down an explicit operator on the chiral de Rham complex of a Calabi-Yau variety <em>X</em> which intertwines the usual <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span> module structure with its twist by the spectral flow automorphism of the <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span>, producing the expected <em>spectral flow equivariance</em>. Taking the trace of the operators <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>J</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> on cohomology, and using the obvious interaction of spectral flow with characters, we obtain an explicit categorification of ellipticity of the elliptic genus of <em>X</em>, which is well known by other means.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108156"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a new technique to describe partial reductions and inverse Hamiltonian reductions between affine -algebras along the closure relations of associated nilpotent orbits in the case of , fulfilling all the missing constructions in the literature. We also apply the partial reductions to modules in the Kazhdan–Lusztig category and show compatibility with the usual reductions of Weyl modules.
{"title":"Connecting affine W-algebras: A case study on sl4","authors":"Justine Fasquel , Zachary Fehily , Ethan Fursman , Shigenori Nakatsuka","doi":"10.1016/j.jpaa.2025.108149","DOIUrl":"10.1016/j.jpaa.2025.108149","url":null,"abstract":"<div><div>We introduce a new technique to describe partial reductions and inverse Hamiltonian reductions between affine <span><math><mi>W</mi></math></span>-algebras along the closure relations of associated nilpotent orbits in the case of <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>, fulfilling all the missing constructions in the literature. We also apply the partial reductions to modules in the Kazhdan–Lusztig category and show compatibility with the usual reductions of Weyl modules.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108149"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108154
Taito Shimoji
Let Γ be a lattice in a simply-connected nilpotent Lie group N whose Lie algebra is p-filiform. We show that Γ is either abelian or 2-step nilpotent if Γ is isomorphic to the fundamental group of a smooth complex algebraic variety. Moreover as an application of our result, we give a required condition of a lattice in a simply-connected nilpotent Lie group of dimension less than or equal to six to be isomorphic to the fundamental group of a smooth complex algebraic variety.
{"title":"Gradings on nilpotent Lie algebras associated with the nilpotent fundamental groups of smooth complex algebraic varieties","authors":"Taito Shimoji","doi":"10.1016/j.jpaa.2025.108154","DOIUrl":"10.1016/j.jpaa.2025.108154","url":null,"abstract":"<div><div>Let Γ be a lattice in a simply-connected nilpotent Lie group <em>N</em> whose Lie algebra <span><math><mi>n</mi></math></span> is <em>p</em>-filiform. We show that Γ is either abelian or 2-step nilpotent if Γ is isomorphic to the fundamental group of a smooth complex algebraic variety. Moreover as an application of our result, we give a required condition of a lattice in a simply-connected nilpotent Lie group of dimension less than or equal to six to be isomorphic to the fundamental group of a smooth complex algebraic variety.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108154"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108150
Klaus Mattis, Timo Weiß
For an endofunctor on an (∞-)category we define the ∞-category of generalized Cartier modules as the lax equalizer of F and the identity. This generalizes the notion of Cartier modules on -schemes considered in [4]. We show that in favorable cases is monadic over . If is a Grothendieck abelian category and is an exact and colimit-preserving endofunctor, we use this fact to construct an equivalence of stable ∞-categories. We use this equivalence to construct a perverse t-structure on for any Noetherian -scheme X with absolute Frobenius F. If F is finite, this coincides with the perverse t-structure constructed in [3].
{"title":"The derived ∞-category of Cartier modules","authors":"Klaus Mattis, Timo Weiß","doi":"10.1016/j.jpaa.2025.108150","DOIUrl":"10.1016/j.jpaa.2025.108150","url":null,"abstract":"<div><div>For an endofunctor <span><math><mi>F</mi><mo>:</mo><mi>C</mi><mo>→</mo><mi>C</mi></math></span> on an (∞-)category <span><math><mi>C</mi></math></span> we define the ∞-category <span><math><mi>Cart</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> of generalized Cartier modules as the lax equalizer of <em>F</em> and the identity. This generalizes the notion of Cartier modules on <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-schemes considered in <span><span>[4]</span></span>. We show that in favorable cases <span><math><mi>Cart</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> is monadic over <span><math><mi>C</mi></math></span>. If <span><math><mi>A</mi></math></span> is a Grothendieck abelian category and <span><math><mi>F</mi><mo>:</mo><mi>A</mi><mo>→</mo><mi>A</mi></math></span> is an exact and colimit-preserving endofunctor, we use this fact to construct an equivalence <span><math><mi>D</mi><mo>(</mo><mi>Cart</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>F</mi><mo>)</mo><mo>)</mo><mo>≃</mo><mi>Cart</mi><mo>(</mo><mi>D</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>,</mo><mi>D</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>)</mo></math></span> of stable ∞-categories. We use this equivalence to construct a perverse t-structure on <span><math><mi>D</mi><mo>(</mo><mi>Cart</mi><mo>(</mo><mi>Mod</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>)</mo><mo>)</mo></math></span> for any Noetherian <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-scheme <em>X</em> with absolute Frobenius <em>F</em>. If <em>F</em> is finite, this coincides with the perverse t-structure constructed in <span><span>[3]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108150"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108152
Benjamin Katz, Andrew J. Soto Levins
This work concerns an Ext analog of the classical Euler characteristic of a pair of finitely generated modules over commutative noetherian local rings.
本文研究了交换诺瑟局部环上一对有限生成模的经典欧拉特征的Ext模拟。
{"title":"On the ext analog of the Euler characteristic","authors":"Benjamin Katz, Andrew J. Soto Levins","doi":"10.1016/j.jpaa.2025.108152","DOIUrl":"10.1016/j.jpaa.2025.108152","url":null,"abstract":"<div><div>This work concerns an Ext analog of the classical Euler characteristic of a pair of finitely generated modules over commutative noetherian local rings.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108152"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.jpaa.2025.108147
Aranya Lahiri , Claus Sorensen , Matthias Strauch
Let be a p-saturated group and a complete and discretely valued extension. In this paper we introduce the space of K-valued overconvergent functions . In the process we promote the rigid analytic group attached to in [13] to a dagger group. A main result of this article is that under certain assumptions (satisfied for example when G is a uniform pro-p group) the distribution algebra , i.e. the strong dual of , is a Fréchet-Stein algebra in the sense of [21].
In the last section we introduce overconvergent representations and show that there is an anti-equivalence of categories between overconvergent G-representations of compact type and continuous -modules on nuclear Fréchet spaces. This is analogous to the anti-equivalence between locally analytic representations and modules over the locally analytic distribution algebra as proved in [20].
{"title":"Dagger groups and p-adic distribution algebras","authors":"Aranya Lahiri , Claus Sorensen , Matthias Strauch","doi":"10.1016/j.jpaa.2025.108147","DOIUrl":"10.1016/j.jpaa.2025.108147","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> be a <em>p</em>-saturated group and <span><math><mi>K</mi><mo>/</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> a complete and discretely valued extension. In this paper we introduce the space of <em>K</em>-valued <em>overconvergent</em> functions <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>. In the process we promote the rigid analytic group attached to <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> in <span><span>[13]</span></span> to a dagger group. A main result of this article is that under certain assumptions (satisfied for example when <em>G</em> is a uniform pro-<em>p</em> group) the distribution algebra <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>, i.e. the strong dual of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>, is a Fréchet-Stein algebra in the sense of <span><span>[21]</span></span>.</div><div>In the last section we introduce overconvergent representations and show that there is an anti-equivalence of categories between overconvergent <em>G</em>-representations of compact type and continuous <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>-modules on nuclear Fréchet spaces. This is analogous to the anti-equivalence between locally analytic representations and modules over the locally analytic distribution algebra as proved in <span><span>[20]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108147"},"PeriodicalIF":0.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-05DOI: 10.1016/j.jpaa.2025.108155
Adele Maltempo , Carolina Vallejo
Let N be normal subgroup of a finite group G, p be a prime, P be a Sylow p-subgroup of G and θ be a P-invariant irreducible character of N. Suppose that is a p-solvable group. In this note we show that, whenever a finite group A acts on G stabilizing P, there exists an A-equivariant McKay bijection between irreducible characters lying over θ of degree prime to p of G and . This is a consequence of a recent result of D. Rossi. Our approach here is independent from Rossi's and follows the original idea of the proof of the McKay conjecture for p-solvable groups. In particular, we rely on the so-called Okuyama-Wajima argument to deal with characters above Glauberman correspondents. For this purpose, we generalize a classical result of P. X. Gallagher on the number of irreducible characters of G lying over θ.
{"title":"The McKay conjecture with group automorphisms and the Okuyama-Wajima argument","authors":"Adele Maltempo , Carolina Vallejo","doi":"10.1016/j.jpaa.2025.108155","DOIUrl":"10.1016/j.jpaa.2025.108155","url":null,"abstract":"<div><div>Let <em>N</em> be normal subgroup of a finite group <em>G</em>, <em>p</em> be a prime, <em>P</em> be a Sylow <em>p</em>-subgroup of <em>G</em> and <em>θ</em> be a <em>P</em>-invariant irreducible character of <em>N</em>. Suppose that <span><math><mi>G</mi><mo>/</mo><mi>N</mi></math></span> is a <em>p</em>-solvable group. In this note we show that, whenever a finite group <em>A</em> acts on <em>G</em> stabilizing <em>P</em>, there exists an <em>A</em>-equivariant McKay bijection between irreducible characters lying over <em>θ</em> of degree prime to <em>p</em> of <em>G</em> and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>P</mi><mo>)</mo><mi>N</mi></math></span>. This is a consequence of a recent result of D. Rossi. Our approach here is independent from Rossi's and follows the original idea of the proof of the McKay conjecture for <em>p</em>-solvable groups. In particular, we rely on the so-called Okuyama-Wajima argument to deal with characters above Glauberman correspondents. For this purpose, we generalize a classical result of P. X. Gallagher on the number of irreducible characters of <em>G</em> lying over <em>θ</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108155"},"PeriodicalIF":0.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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