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A remark on the paper of Deninger and Murre 对 Deninger 和 Murre 论文的评论
Indagationes Mathematicae Pub Date : 2024-07-01 DOI: 10.1016/j.indag.2024.07.010
Ben Moonen
{"title":"A remark on the paper of Deninger and Murre","authors":"Ben Moonen","doi":"10.1016/j.indag.2024.07.010","DOIUrl":"https://doi.org/10.1016/j.indag.2024.07.010","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"17 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141844337","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: 1
A note on Lp-factorizations of representations 关于表征的 Lp 因子化的说明
Indagationes Mathematicae Pub Date : 2024-07-01 DOI: 10.1016/j.indag.2024.07.002
Pritam Ganguly, Bernhard Krötz, Job J. Kuit
{"title":"A note on <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e22\" altimg=\"si3.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math>-factorizations of representations","authors":"Pritam Ganguly, Bernhard Krötz, Job J. Kuit","doi":"10.1016/j.indag.2024.07.002","DOIUrl":"https://doi.org/10.1016/j.indag.2024.07.002","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717121","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 singularity of type E7 and the complex reflection group ST34 E7 型简单奇点和复反射群 ST34
Indagationes Mathematicae Pub Date : 2024-07-01 DOI: 10.1016/j.indag.2024.07.008
Jiro Sekiguchi
{"title":"Simple singularity of type <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e21\" altimg=\"si3.svg\"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn></mml:mrow></mml:msub></mml:math> and the complex reflection group ST34","authors":"Jiro Sekiguchi","doi":"10.1016/j.indag.2024.07.008","DOIUrl":"https://doi.org/10.1016/j.indag.2024.07.008","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"108 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141714375","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
Symmetry breaking operators for the reductive dual pair (U[formula omitted],U[formula omitted]) 还原对偶（U[式略],U[式略]）的对称破缺算子
Indagationes Mathematicae Pub Date : 2024-06-28 DOI: 10.1016/j.indag.2024.06.004
M. McKee, A. Pasquale, T. Przebinda
{"title":"Symmetry breaking operators for the reductive dual pair (U[formula omitted],U[formula omitted])","authors":"M. McKee, A. Pasquale, T. Przebinda","doi":"10.1016/j.indag.2024.06.004","DOIUrl":"https://doi.org/10.1016/j.indag.2024.06.004","url":null,"abstract":"We consider the dual pair in the symplectic group . Fix a Weil representation of the metaplectic group . Let and be the preimages of and in , and let be a genuine irreducible representation of . We study the Weyl symbol of the (unique up to a possibly zero constant) symmetry breaking operator (SBO) intertwining the Weil representation with . This SBO coincides with the orthogonal projection of the space of the Weil representation onto its -isotypic component and also with the orthogonal projection onto its -isotypic component. Hence can be computed in two different ways, one using and the other using . By matching the results, we recover Weyl’s theorem stating that occurs in the Weil representation with multiplicity at most one and we also recover the complete list of the representations occurring in Howe’s correspondence.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141569877","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
Sharp estimates for distinguished random walks on affine buildings of type [formula omitted] 型仿射建筑物上杰出随机游走的锐估计 [公式省略]
Indagationes Mathematicae Pub Date : 2024-06-13 DOI: 10.1016/j.indag.2024.06.002
Jean-Philippe Anker, Bruno Schapira, Bartosz Trojan
{"title":"Sharp estimates for distinguished random walks on affine buildings of type [formula omitted]","authors":"Jean-Philippe Anker, Bruno Schapira, Bartosz Trojan","doi":"10.1016/j.indag.2024.06.002","DOIUrl":"https://doi.org/10.1016/j.indag.2024.06.002","url":null,"abstract":"We study a distinguished random walk on affine buildings of type , which was already considered by Cartwright, Saloff-Coste and Woess. In rank , it is the simple random walk and we obtain optimal global bounds for its transition density (same upper and lower bound, up to multiplicative constants). In the higher rank case, we obtain sharp uniform bounds in fairly large space–time regions which are sufficient for most applications.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504917","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 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
Indagationes Mathematicae Pub Date : 2024-06-08 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":"https://doi.org/10.1016/j.indag.2024.05.012","url":null,"abstract":"For every simple Hermitian Lie group , we consider a certain maximal parabolic subgroup whose unipotent radical is either abelian (if is of tube type) or two-step nilpotent (if is of non-tube type). By the generalized Whittaker Plancherel formula we mean the Plancherel decomposition of , the space of square-integrable sections of the homogeneous vector bundle over associated with an irreducible unitary representation of . Assuming that the central character of is contained in a certain cone, we construct embeddings of all holomorphic discrete series representations of into and show that the multiplicities are equal to the dimensions of the lowest -types. The construction is in terms of a kernel function which can be explicitly defined using certain projections inside a complexification of . This kernel function carries all information about the holomorphic discrete series embedding, the lowest -type as functions on , as well as the associated Whittaker vectors.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"161 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504920","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
Cartan–Helgason theorem for quaternionic symmetric and twistor spaces 四元对称空间和扭转空间的 Cartan-Helgason 定理
Indagationes Mathematicae Pub Date : 2024-06-06 DOI: 10.1016/j.indag.2024.05.013
Clemens Weiske, Jun Yu, Genkai Zhang
{"title":"Cartan–Helgason theorem for quaternionic symmetric and twistor spaces","authors":"Clemens Weiske, Jun Yu, Genkai Zhang","doi":"10.1016/j.indag.2024.05.013","DOIUrl":"https://doi.org/10.1016/j.indag.2024.05.013","url":null,"abstract":"Let be a complex quaternionic symmetric pair with having an ideal , . Consider the representation of via the projection onto the ideal . We study the finite dimensional irreducible representations of which contain under . We give a characterization of all such representations and find the corresponding multiplicity, the dimension of We consider also the branching problem of under and find the multiplicities. Geometrically the Lie subalgebra defines a twistor space over the compact symmetric space of the compact real form of , , and our results give the decomposition for the -spaces of sections of certain vector bundles over the symmetric space and line bundles over the twistor space. This generalizes Cartan–Helgason’s theorem for symmetric spaces and Schlichtkrull’s theorem for Hermitian symmetric spaces where one-dimensional representations of are considered.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552929","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
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
Indagationes Mathematicae Pub Date : 2024-06-04 DOI: 10.1016/j.indag.2024.05.011
Kazufumi Kimoto, Masato Wakayama
{"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":"https://doi.org/10.1016/j.indag.2024.05.011","url":null,"abstract":"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 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 -adically convergent series defined by the -adic Hurwitz zeta function.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550825","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
Dynamical systems for arithmetic schemes 算术方案的动力系统
Indagationes Mathematicae Pub Date : 2024-06-01 DOI: 10.1016/j.indag.2024.05.007
Christopher Deninger
{"title":"Dynamical systems for arithmetic schemes","authors":"Christopher Deninger","doi":"10.1016/j.indag.2024.05.007","DOIUrl":"https://doi.org/10.1016/j.indag.2024.05.007","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141513686","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
Some remarks on the smash-nilpotence conjecture 关于粉碎零势猜想的一些评论
Indagationes Mathematicae Pub Date : 2024-06-01 DOI: 10.1016/j.indag.2024.05.009
Bruno Kahn
{"title":"Some remarks on the smash-nilpotence conjecture","authors":"Bruno Kahn","doi":"10.1016/j.indag.2024.05.009","DOIUrl":"https://doi.org/10.1016/j.indag.2024.05.009","url":null,"abstract":"We discuss cases where Voevodsky’s smash nilpotence conjecture is known, and give a few new ones. In particular we explain a theorem of the cube for 1-cycles, which is due to Oussama Ouriachi.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141553293","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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