Indagationes Mathematicae-New Series最新文献_第2页

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

Indagationes Mathematicae-New Series Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.05.002

Mengyuan Cao, Monica Nevins, Hadi Salmasian

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

Indagationes Mathematicae-New Series Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.05.012

Jan Frahm , Gestur Ólafsson , Bent Ørsted

{"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

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

Indagationes Mathematicae-New Series Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.04.005

Maarten Solleveld

{"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

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

Indagationes Mathematicae-New Series Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.05.001

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

引用次数: 0

A construction of solutions of an integrable deformation of a commutative Lie algebra of skew hermitian Z×Z-matrices 倾斜[式略]-赫米特矩阵的交换李代数可积分变形解的构造

IF 0.5 4区数学

Indagationes Mathematicae-New Series Pub Date : 2025-01-01 DOI: 10.1016/j.indag.2024.04.001

Aloysius G. Helminck , Gerardus F. Helminck

引用次数: 0

Alternating multiple mixed values: Regularization, special values, parity, and dimension conjectures 交替多重混合值：正则化、特殊值、奇偶性和维度猜想

IF 0.5 4区数学

Indagationes Mathematicae-New Series Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.06.001

{"title":"Alternating multiple mixed values: Regularization, special values, parity, and dimension conjectures","authors":"","doi":"10.1016/j.indag.2024.06.001","DOIUrl":"10.1016/j.indag.2024.06.001","url":null,"abstract":"<div><div>In this paper, we define and study a variant of multiple zeta values (MZVs) of level four, called alternating multiple mixed values or alternating multiple <span><math><mi>M</mi></math></span>-values (AMMVs), forming a <span><math><mrow><mi>Q</mi><mrow><mo>[</mo><mi>i</mi><mo>]</mo></mrow></mrow></math></span>-subspace of the colored MZVs of level four. This variant includes the alternating version of Hoffman’s multiple <span><math><mi>t</mi></math></span>-values, Kaneko–Tsumura’s multiple <span><math><mi>T</mi></math></span>-values, and the multiple <span><math><mi>S</mi></math></span>-values studied by the authors previously as special cases. We exhibit nice properties similar to the ordinary MZVs such as the generalized duality, integral shuffle and series stuffle relations. After setting up the algebraic framework we derive the regularized double shuffle relations of the AMMVs by adopting the machinery from color MZVs of level four. As an important application, we prove a parity result for AMMVs previously conjectured by two of us. We also investigate several alternating multiple <span><math><mi>S</mi></math></span>- and <span><math><mi>T</mi></math></span>-values by establishing some explicit relations of integrals involving arctangent function. At the end, we compute the dimensions of a few interesting subspaces of AMMVs for weight less than 9. Supported by theoretical and numerical evidence aided by numerical and symbolic computation, we formulate a few conjectures concerning the dimensions of the above-mentioned subspaces of AMMVs. These conjectures hint at a few very rich but previously overlooked algebraic and geometric structures associated with these vector spaces.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 6","pages":"Pages 1212-1248"},"PeriodicalIF":0.5,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504919","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

Class numbers, Ono invariants and some interesting primes 类数、小野不变式和一些有趣的素数

IF 0.5 4区数学

Indagationes Mathematicae-New Series Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.06.003

{"title":"Class numbers, Ono invariants and some interesting primes","authors":"","doi":"10.1016/j.indag.2024.06.003","DOIUrl":"10.1016/j.indag.2024.06.003","url":null,"abstract":"<div><div>Our aim is to find all the prime numbers <span><math><mi>p</mi></math></span> such that <span><math><mrow><mi>p</mi><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> has at most two different prime factors, for all the odd integers <span><math><mi>x</mi></math></span> such that <span><math><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>≤</mo><mi>p</mi></mrow></math></span>. We solve entirely the cases <span><math><mrow><mi>p</mi><mo>≡</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mspace></mspace><mrow><mo>(</mo><mo>mod</mo><mspace></mspace><mn>8</mn><mo>)</mo></mrow></mrow></math></span>, using the knowledge of the quadratic imaginary number fields with class numbers 4, 1 and 2 respectively. The case <span><math><mrow><mi>p</mi><mo>≡</mo><mn>7</mn><mspace></mspace><mrow><mo>(</mo><mo>mod</mo><mspace></mspace><mn>8</mn><mo>)</mo></mrow></mrow></math></span> is not completely solved. Taking into account a result of Stéphane Louboutin, we prove that there is at most one value <span><math><mrow><mi>p</mi><mo>≡</mo><mn>7</mn><mspace></mspace><mrow><mo>(</mo><mo>mod</mo><mspace></mspace><mn>8</mn><mo>)</mo></mrow></mrow></math></span> besides our list. Assuming a Restricted Riemann Hypothesis, the list is complete. In the last section of the paper we give a short sketch for the general problem: find all odd integers <span><math><mrow><mi>n</mi><mo>></mo><mn>1</mn></mrow></math></span> such that <span><math><mrow><mi>n</mi><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> has at most two different prime factors, for all the odd integers <span><math><mi>x</mi></math></span> such that <span><math><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>≤</mo><mi>n</mi></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 6","pages":"Pages 1249-1258"},"PeriodicalIF":0.5,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504918","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

Integral expressions for Schur multiple zeta values 舒尔多重zeta值的积分表达式

IF 0.5 4区数学

Indagationes Mathematicae-New Series Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.05.010

引用次数: 0

Simple modules for untwisted affine Lie algebras induced from nilpotent loop subalgebras 由零能环子布拉诱导的非扭曲仿射李代数的简单模块

IF 0.5 4区数学

Indagationes Mathematicae-New Series Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.05.003

引用次数: 0

Functorial splitting of l-adic cohomology of an extension of group varieties 群变种扩展的[公式省略]-自洽同调的函数分裂

IF 0.5 4区数学

Indagationes Mathematicae-New Series Pub Date : 2024-11-01 DOI: 10.1016/j.indag.2024.05.006

引用次数: 0