Indagationes Mathematicae-New Series最新文献

英文中文

Partition functions for non-commutative harmonic oscillators and related divergent series 非交换调和振荡器的分割函数及相关发散级数

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.05.011

Kazufumi Kimoto , Masato Wakayama

In the standard normalization, the eigenvalues of the quantum harmonic oscillator are given by positive half-integers with the Hermite functions as eigenfunctions. Thus, its spectral zeta function is essentially given by the Riemann zeta function. The heat kernel (or propagator) of the quantum harmonic oscillator (qHO) is given by the Mehler formula, and the partition function is obtained by taking its trace. In general, the spectral zeta function of the given system is obtained by the Mellin transform of its partition function. In the case of non-commutative harmonic oscillators (NCHO), however, the heat kernel and partition functions are still unknown, although meromorphic continuation of the corresponding spectral zeta function and special values at positive integer points have been studied. On the other hand, explicit formulas for the heat kernel and partition function have been obtained for the quantum Rabi model (QRM), which is the simplest and most fundamental model for light and matter interaction in addition to having the NCHO as a covering model. In this paper, we propose a notion of the quasi-partition function for a quantum interaction model if the corresponding spectral zeta function can be meromorphically continued to the whole complex plane. The quasi-partition function for qHO and QRM actually gives the partition function. Assuming that this holds for the NCHO (currently a conjecture), we can find various interesting properties for the spectrum of the NCHO. Moreover, although we cannot expect any functional equation of the spectral zeta function for the quantum interaction models, we try to seek if there is some relation between the special values at positive and negative points. Attempting to seek this, we encounter certain divergent series expressing formally the Hurwitz zeta function by calculating integrals of the partition functions. We then give two interpretations of these divergent series by the Borel summation and

p

-adically convergent series defined by the

p

-adic Hurwitz zeta function.

在标准归一化中，量子谐振子的特征值由正半整数给出，Hermite 函数为特征函数。因此，它的谱zeta函数基本上是由黎曼zeta函数给出的。量子谐振子（qHO）的热核（或传播者）由梅勒公式给出，分割函数则通过求其迹线得到。一般来说，给定系统的谱zeta函数由其分割函数的梅林变换得到。然而，在非交换谐振子（NCHO）的情况下，热核和分割函数仍然是未知的，尽管人们已经研究了相应谱zeta函数的非定常延续以及在正整数点的特殊值。另一方面，量子拉比模型（QRM）的热核和分区函数的明确公式已经得到，该模型是光与物质相互作用的最简单和最基本的模型，此外还以 NCHO 作为覆盖模型。在本文中，我们提出了一个量子相互作用模型的准分区函数的概念，即如果相应的谱zeta函数可以在整个复平面上进行分形延续，则该模型的准分区函数可以在整个复平面上进行分形延续。qHO 和 QRM 的准分区函数实际上给出了分区函数。假设这一点对 NCHO 成立（目前只是一种猜想），我们就能发现 NCHO 谱的各种有趣性质。此外，尽管我们不能指望量子相互作用模型的谱 zeta 函数有任何函数方程，但我们还是试图寻找正负点的特殊值之间是否存在某种关系。为了寻求这种关系，我们遇到了某些发散级数，它们通过计算分区函数的积分来正式表达赫维茨zeta函数。然后，我们给出了这些发散级数的两种解释：伯累尔求和和由-adic Hurwitz zeta 函数定义的-adically 收敛级数。

{"title":"Partition functions for non-commutative harmonic oscillators and related divergent series","authors":"Kazufumi Kimoto , Masato Wakayama","doi":"10.1016/j.indag.2024.05.011","DOIUrl":"10.1016/j.indag.2024.05.011","url":null,"abstract":"<div><div><span><span>In the standard normalization, the eigenvalues of the quantum harmonic oscillator<span> are given by positive half-integers with the Hermite functions as eigenfunctions<span>. Thus, its spectral zeta function is essentially given by the Riemann zeta function. The heat kernel (or propagator) of the quantum harmonic oscillator (qHO) is given by the Mehler formula, and the </span></span></span>partition function is obtained by taking its trace. In general, the spectral zeta function of the given system is obtained by the Mellin transform of its partition function. In the case of non-commutative harmonic oscillators (NCHO), however, the heat kernel and partition functions are still unknown, although meromorphic continuation of the corresponding spectral zeta function and special values at positive integer points have been studied. On the other hand, explicit formulas for the heat kernel and partition function have been obtained for the quantum Rabi model (QRM), which is the simplest and most fundamental model for light and matter interaction in addition to having the NCHO as a covering model. In this paper, we propose a notion of the </span><em>quasi-partition function</em> for a quantum interaction model if the corresponding spectral zeta function can be meromorphically continued to the whole complex plane. The quasi-partition function for qHO and QRM actually gives the partition function. Assuming that this holds for the NCHO (currently a conjecture), we can find various interesting properties for the spectrum of the NCHO. Moreover, although we cannot expect any functional equation of the spectral zeta function for the quantum interaction models, we try to seek if there is some relation between the special values at positive and negative points. Attempting to seek this, we encounter certain divergent series expressing formally the Hurwitz zeta function by calculating integrals of the partition functions. We then give two interpretations of these divergent series by the Borel summation and <span><math><mi>p</mi></math></span>-adically convergent series defined by the <span><math><mi>p</mi></math></span>-adic Hurwitz zeta function.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 1","pages":"Pages 302-336"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Holomorphic Laplacian on the Lie ball and the Penrose transform 李球上的全态拉普拉斯和彭罗斯变换

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.04.004

Hideko Sekiguchi

We prove that any holomorphic function

f

on the Lie ball of even dimension satisfying

Δ f = 0

is obtained uniquely by the higher-dimensional Penrose transform of a Dolbeault cohomology for a twisted line bundle of a certain domain of the Grassmannian of isotropic subspaces. To overcome the difficulties arising from our setting that the line bundle parameter is outside the good range, we use some techniques from algebraic representation theory.

我们证明，在满足偶数维的Lie球上的任何全形函数，都可以通过各向同性子空间的格拉斯曼的某个域的扭曲线束的多尔贝同调的高维彭罗斯变换唯一地得到。为了克服线束参数为，这一设定所带来的困难，我们使用了代数表示理论中的一些技术。

引用次数: 0

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01

引用次数: 0

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01

引用次数: 0

The refined solution to the Capelli eigenvalue problem for gl(m|n)⊕gl(m|n) and gl(m|2n) gl(m|n<mml)的卡佩利特征值问题的精解

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.05.002

Mengyuan Cao, Monica Nevins, Hadi Salmasian

Let

g

be either the Lie superalgebra

gl (V) \oplus gl (V)

where

V ≔ ℂ^{m | n}

or the Lie superalgebra

gl (V)

where

V ≔ ℂ^{m | 2 n}

. Furthermore, let

W

be the

g

-module defined by

W ≔ V \otimes V^{*}

in the former case and

W ≔ S^{2} (V)

in the latter case. Associated to

(g, W)

there exists a distinguished basis of Capelli operators

{D^{λ}}_{λ \in Ω}

, naturally indexed by a set of hook partitions

Ω

, for the subalgebra of

g

-invariants in the superalgebra

PD (W)

of superdifferential operators on

W

Let

b

be a Borel subalgebra of

g

. We compute eigenvalues of the

D^{λ}

on the irreducible

g

-submodules of

P (W)

and obtain them explicitly as the evaluation of the interpolation super Jack polynomials of Sergeev–Veselov at suitable affine functions of the

b

-highest weight. While the former case is straightforward, the latter is significantly more complex. This generalizes a result by Sahi, Salmasian and Serganova for these cases, where such formulas were given for a fixed choice of Borel subalgebra.

设g为李超代数gl(V)⊕gl(V)，其中V是对象中包含的向量，其中V是对象中包含的向量，其中V是对象中包含的向量。更进一步，设W为g模，其中W在前一种情况下是W，在后一种情况下是W， W在前一种情况下是V⊗V *， W在后一种情况下是W，是S2(V)。相关(g, W)存在一个杰出的基础卡佩里运营商{Dλ}λ∈Ω,自然被一组钩子分区Ω,子代数的g-invariants superdifferential superalgebra PD (W)的运营商W.Let b是一个波莱尔的子代数g。我们计算特征值D的不可约g-submodulesλP (W),得到他们明确的评价插值超级杰克Sergeev-Veselov在合适的仿射函数的多项式b-highest重量。前一种情况很简单，而后一种情况要复杂得多。这推广了Sahi， Salmasian和Serganova在这些情况下的结果，在这些情况下，这些公式是针对固定选择的Borel子代数给出的。

引用次数: 0

The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula II. Non-tube type groups 全形离散级数对广义惠特克-普朗切尔公式的贡献 II.非管型群

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.05.012

Jan Frahm , Gestur Ólafsson , Bent Ørsted

For every simple Hermitian Lie group

G

, we consider a certain maximal parabolic subgroup whose unipotent radical

N

is either abelian (if

G

is of tube type) or two-step nilpotent (if

G

is of non-tube type). By the generalized Whittaker Plancherel formula we mean the Plancherel decomposition of

L^{2} (G / N, ω)

, the space of square-integrable sections of the homogeneous vector bundle over

G / N

associated with an irreducible unitary representation

ω

N

. Assuming that the central character of

ω

is contained in a certain cone, we construct embeddings of all holomorphic discrete series representations of

G

into

L^{2} (G / N, ω)

and show that the multiplicities are equal to the dimensions of the lowest

K

-types. The construction is in terms of a kernel function which can be explicitly defined using certain projections inside a complexification of

G

. This kernel function carries all information about the holomorphic discrete series embedding, the lowest

K

-type as functions on

G / N

, as well as the associated Whittaker vectors.

对于每一个简单赫米蒂李群，我们都考虑某个最大抛物线子群，它的单势根要么是无性的（如果是管型），要么是两步零势的（如果是非管型）。通过广义惠特克-普朗切尔公式，我们指的是普朗切尔分解，即与.的不可还原单元代表相关联的均相向量束的平方可积分截面空间。假设.的中心特征包含在某个锥体中，我们构造了.的所有全形离散序列代表的嵌入，并证明其乘数等于最低类型的维数。这个核函数包含了全态离散级数嵌入的所有信息、作为函数的最低类型以及相关的惠特克向量。

{"title":"The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula II. Non-tube type groups","authors":"Jan Frahm , Gestur Ólafsson , Bent Ørsted","doi":"10.1016/j.indag.2024.05.012","DOIUrl":"10.1016/j.indag.2024.05.012","url":null,"abstract":"<div><div>For every simple Hermitian Lie group <span><math><mi>G</mi></math></span>, we consider a certain maximal parabolic subgroup whose unipotent radical <span><math><mi>N</mi></math></span> is either abelian (if <span><math><mi>G</mi></math></span> is of tube type) or two-step nilpotent (if <span><math><mi>G</mi></math></span> is of non-tube type). By the generalized Whittaker Plancherel formula we mean the Plancherel decomposition of <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>G</mi><mo>/</mo><mi>N</mi><mo>,</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math></span>, the space of square-integrable sections of the homogeneous vector bundle over <span><math><mrow><mi>G</mi><mo>/</mo><mi>N</mi></mrow></math></span> associated with an irreducible unitary representation <span><math><mi>ω</mi></math></span> of <span><math><mi>N</mi></math></span>. Assuming that the central character of <span><math><mi>ω</mi></math></span> is contained in a certain cone, we construct embeddings of all holomorphic discrete series representations of <span><math><mi>G</mi></math></span> into <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>G</mi><mo>/</mo><mi>N</mi><mo>,</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> and show that the multiplicities are equal to the dimensions of the lowest <span><math><mi>K</mi></math></span>-types. The construction is in terms of a kernel function which can be explicitly defined using certain projections inside a complexification of <span><math><mi>G</mi></math></span>. This kernel function carries all information about the holomorphic discrete series embedding, the lowest <span><math><mi>K</mi></math></span>-type as functions on <span><math><mrow><mi>G</mi><mo>/</mo><mi>N</mi></mrow></math></span>, as well as the associated Whittaker vectors.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 1","pages":"Pages 337-356"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01

引用次数: 0

Parameters of Hecke algebras for Bernstein components of p-adic groups p-adic 群伯恩斯坦成分的赫克代数参数

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.04.005

Maarten Solleveld

Let

G

be a reductive group over a non-archimedean local field

F

. Consider an arbitrary Bernstein block

Rep {(G)}^{s}

in the category of complex smooth

G

-representations. In earlier work the author showed that there exists an affine Hecke algebra

H (O, G)

whose category of right modules is closely related to

Rep {(G)}^{s}

. In many cases this is in fact an equivalence of categories, like for Iwahori-spherical representations.

In this paper we study the

q

-parameters of the affine Hecke algebras

H (O, G)

. We compute them in many cases, in particular for principal series representations of quasi-split groups and for classical groups.

Lusztig conjectured that the

q

-parameters are always integral powers of the cardinality of the residue field of

F

, and that they coincide with the

q

-parameters coming from some Bernstein block of unipotent representations. We reduce this conjecture to the case of absolutely simple

p

-adic groups, and we prove it for most of those.

设G是非阿基米德局部域f上的约化群，考虑复光滑G表示范畴中的任意Bernstein块Rep(G)s。作者在前期工作中证明了存在一个仿射Hecke代数H(O，G)，其右模的范畴与Rep(G)s密切相关。在许多情况下，这实际上是范畴的等价，就像iwahori -球面表示。本文研究仿射Hecke代数H（O，G）的q参数。我们在许多情况下计算了它们，特别是对于拟分裂群和经典群的主级数表示。Lusztig推测q-参数总是F的残馀域的基数的整数幂，并且它们与来自某个Bernstein块的单幂表示的q-参数一致。我们把这个猜想简化到绝对简单的p进群的情况下，并对大多数这种情况进行了证明。

{"title":"Parameters of Hecke algebras for Bernstein components of p-adic groups","authors":"Maarten Solleveld","doi":"10.1016/j.indag.2024.04.005","DOIUrl":"10.1016/j.indag.2024.04.005","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span> be a reductive group over a non-archimedean local field <span><math><mi>F</mi></math></span>. Consider an arbitrary Bernstein block <span><math><mrow><mi>Rep</mi><msup><mrow><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup></mrow></math></span> in the category of complex smooth <span><math><mi>G</mi></math></span>-representations. In earlier work the author showed that there exists an affine Hecke algebra <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>O</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> whose category of right modules is closely related to <span><math><mrow><mi>Rep</mi><msup><mrow><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup></mrow></math></span>. In many cases this is in fact an equivalence of categories, like for Iwahori-spherical representations.</div><div>In this paper we study the <span><math><mi>q</mi></math></span>-parameters of the affine Hecke algebras <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>O</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. We compute them in many cases, in particular for principal series representations of quasi-split groups and for classical groups.</div><div>Lusztig conjectured that the <span><math><mi>q</mi></math></span>-parameters are always integral powers of the cardinality of the residue field of <span><math><mi>F</mi></math></span>, and that they coincide with the <span><math><mi>q</mi></math></span>-parameters coming from some Bernstein block of unipotent representations. We reduce this conjecture to the case of absolutely simple <span><math><mi>p</mi></math></span>-adic groups, and we prove it for most of those.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 1","pages":"Pages 124-170"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140778482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01

引用次数: 0

Spectral correspondences for finite graphs without dead ends 无死角有限图谱的谱对应关系

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.05.001

K.-U. Bux , J. Hilgert , T. Weich

We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on vector spaces associated with the set of non-backtracking paths in the graphs. The second kind of operators are averaging operators acting on vector spaces associated with the space of vertices of the graph. The choice of vector spaces reflects regularity properties. Our main results are correspondences between classical and quantum spectral objects as well as some automatic regularity properties for eigenfunctions of transfer operators.

我们比较了两类线性算子的频谱特性，它们表征了（经典）大地流及其在无死角连通局部有限图上的量化。第一种是作用于与图中非回溯路径集相关的向量空间的转移算子。第二类算子是作用于与图顶点空间相关的向量空间的平均算子。向量空间的选择反映了正则特性。我们的主要成果是经典和量子光谱对象之间的对应关系，以及转移算子特征函数的一些自动正则特性。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Indagationes Mathematicae-New Series

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀