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Indagationes Mathematicae最新文献

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Limits of Bessel functions for root systems as the rank tends to infinity 根系统贝塞尔函数在秩趋于无穷大时的极限
Indagationes Mathematicae Pub Date : 2024-05-13 DOI: 10.1016/j.indag.2024.05.004
Dominik Brennecken, Margit Rösler
{"title":"Limits of Bessel functions for root systems as the rank tends to infinity","authors":"Dominik Brennecken, Margit Rösler","doi":"10.1016/j.indag.2024.05.004","DOIUrl":"https://doi.org/10.1016/j.indag.2024.05.004","url":null,"abstract":"We study the asymptotic behaviour of Bessel functions associated to root systems of type and type with positive multiplicities as the rank tends to infinity. In both cases, we characterize the possible limit functions and the Vershik–Kerov type sequences of spectral parameters for which such limits exist. In the type case, this gives a new and very natural approach to recent results by Assiotis and Najnudel in the context of -ensembles in random matrix theory. These results generalize known facts about the approximation of the positive-definite Olshanski spherical functions of the space of infinite-dimensional Hermitian matrices over (with the action of the associated infinite unitary group) by spherical functions of finite-dimensional spaces of Hermitian matrices. In the type B case, our results include asymptotic results for the spherical functions associated with the Cartan motion groups of non-compact Grassmannians as the rank goes to infinity, and a classification of the Olshanski spherical functions of the associated inductive limits.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Indagationes Mathematicae Pub Date : 2024-05-11 DOI: 10.1016/j.indag.2024.05.003
Volodymyr Mazorchuk
{"title":"Simple modules for untwisted affine Lie algebras induced from nilpotent loop subalgebras","authors":"Volodymyr Mazorchuk","doi":"10.1016/j.indag.2024.05.003","DOIUrl":"https://doi.org/10.1016/j.indag.2024.05.003","url":null,"abstract":"We construct large families of simple modules for untwisted affine Lie algebras using induction from one-dimensional modules over nilpotent loop subalgebras. We also show that the vector space of the first self-extensions for these module has uncountable dimension and that generic tensor products of these modules are simple.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Chow–Lefschetz motives 周-莱夫谢茨动机
Indagationes Mathematicae Pub Date : 2024-05-03 DOI: 10.1016/j.indag.2024.04.007
Bruno Kahn
{"title":"Chow–Lefschetz motives","authors":"Bruno Kahn","doi":"10.1016/j.indag.2024.04.007","DOIUrl":"https://doi.org/10.1016/j.indag.2024.04.007","url":null,"abstract":"We develop Milne’s theory of Lefschetz motives for general adequate equivalence relations and over a not necessarily algebraically closed base field. The corresponding categories turn out to enjoy all properties predicted by standard and less standard conjectures, in a stronger way: algebraic and numerical equivalences agree in this context. We also compute the Tannakian group associated to a Weil cohomology in a different and more conceptual way than Milne’s case-by-case approach.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multivariate Meixner polynomials related to holomorphic discrete series representations of SU(1, 与 SU(1,</ 的全态离散序列表示相关的多变量梅克斯纳多项式
Indagationes Mathematicae Pub Date : 2024-05-01 DOI: 10.1016/j.indag.2024.04.010
W. Groenevelt, Joop Vermeulen
{"title":"Multivariate Meixner polynomials related to holomorphic discrete series representations of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e20\" altimg=\"si2.svg\"><mml:mrow><mml:mi mathvariant=\"normal\">SU</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</","authors":"W. Groenevelt, Joop Vermeulen","doi":"10.1016/j.indag.2024.04.010","DOIUrl":"https://doi.org/10.1016/j.indag.2024.04.010","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141033600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Becoming a mathematician 成为数学家
Indagationes Mathematicae Pub Date : 2024-05-01 DOI: 10.1016/j.indag.2024.04.009
Gert Heckman
{"title":"Becoming a mathematician","authors":"Gert Heckman","doi":"10.1016/j.indag.2024.04.009","DOIUrl":"https://doi.org/10.1016/j.indag.2024.04.009","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141037961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite odometer factors of rank one group actions 一级群作用的有限里程表因子
Indagationes Mathematicae Pub Date : 2024-05-01 DOI: 10.1016/j.indag.2024.04.012
A. S. Johnson, D. McClendon
{"title":"Finite odometer factors of rank one group actions","authors":"A. S. Johnson, D. McClendon","doi":"10.1016/j.indag.2024.04.012","DOIUrl":"https://doi.org/10.1016/j.indag.2024.04.012","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141032515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The refined solution to the capelli eigenvalue problem for gl(m|n gl(m|n<mml)的卡佩利特征值问题的精解
Indagationes Mathematicae Pub Date : 2024-05-01 DOI: 10.1016/j.indag.2024.05.002
Mengyuan Cao, Monica Nevins, Hadi Salmasian
{"title":"The refined solution to the capelli eigenvalue problem for <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e391\" altimg=\"si22.svg\"><mml:mrow><mml:mi mathvariant=\"fraktur\">gl</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>|</mml:mo><mml:mi>n</mml:mi><mml","authors":"Mengyuan Cao, Monica Nevins, Hadi Salmasian","doi":"10.1016/j.indag.2024.05.002","DOIUrl":"https://doi.org/10.1016/j.indag.2024.05.002","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141034907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Realization of unitary representations of the Lorentz group on de Sitter space 实现洛伦兹群在德西特空间上的单元表征
Indagationes Mathematicae Pub Date : 2024-04-25 DOI: 10.1016/j.indag.2024.04.002
Jan Frahm, Karl-Hermann Neeb, Gestur Ólafsson
{"title":"Realization of unitary representations of the Lorentz group on de Sitter space","authors":"Jan Frahm, Karl-Hermann Neeb, Gestur Ólafsson","doi":"10.1016/j.indag.2024.04.002","DOIUrl":"https://doi.org/10.1016/j.indag.2024.04.002","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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
Indagationes Mathematicae Pub Date : 2024-04-20 DOI: 10.1016/j.indag.2024.04.004
Hideko Sekiguchi
{"title":"Holomorphic Laplacian on the Lie ball and the Penrose transform","authors":"Hideko Sekiguchi","doi":"10.1016/j.indag.2024.04.004","DOIUrl":"https://doi.org/10.1016/j.indag.2024.04.004","url":null,"abstract":"We prove that any holomorphic function on the Lie ball of even dimension satisfying 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 , we use some techniques from algebraic representation theory.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140928520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A construction of solutions of an integrable deformation of a commutative Lie algebra of skew hermitian [formula omitted]-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
Indagationes Mathematicae Pub Date : 2024-04-07 DOI: 10.1016/j.indag.2024.04.001
Aloysius G. Helminck, Gerardus F. Helminck
{"title":"A construction of solutions of an integrable deformation of a commutative Lie algebra of skew hermitian [formula omitted]-matrices","authors":"Aloysius G. Helminck, Gerardus F. Helminck","doi":"10.1016/j.indag.2024.04.001","DOIUrl":"https://doi.org/10.1016/j.indag.2024.04.001","url":null,"abstract":"Inside the algebra of -matrices with coefficients from a commutative -algebra that have only a finite number of nonzero diagonals above the central diagonal, we consider a deformation of a commutative Lie algebra of finite band skew hermitian matrices that is different from the Lie subalgebras that were deformed at the discrete KP hierarchy and its strict version. The evolution equations that the deformed generators of have to satisfy are determined by the decomposition of in the direct sum of an algebra of lower triangular matrices and the finite band skew hermitian matrices. This yields then the -hierarchy. We show that the projections of a solution satisfy zero curvature relations and that it suffices to solve an associated Cauchy problem. Solutions of this type can be obtained by finding appropriate vectors in the -module of oscillating matrices, the so-called wave matrices, that satisfy a set of equations in the oscillating matrices, called the linearization of the -hierarchy. Finally, a Hilbert Lie group will be introduced from which wave matrices for the -hierarchy are constructed. There is a real analogue of the -hierarchy called the -hierarchy. It consists of a deformation of a commutative Lie algebra of anti-symmetric matrices. We will properly introduce it here too on the way and mention everywhere the corresponding result for this hierarchy, but we leave its proofs mostly to the reader.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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