Orbital integrals on GLn x GLn\GL2n

被引：0

作者：

Xue, Hang ^{[1
]}

机构：

[1] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2021年

基金：

美国国家科学基金会;

关键词：

orbital integral; spherical characters; symmetric spaces; CHARACTERS;

D O I：

10.4153/S000841X21000122

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study harmonic analysis on the symmetric space GL(n) x GL(n)\GL(2)(n). We prove several standard results, e.g. Shalika germ expansion of orbital integrals, representability of the Fourier transform of orbital integrals and representability of spherical characters. These properties are not expected to hold for symmetric spaces in general.

引用

页数：29

共 11 条

[1] Orbital integrals on GLn x GLn\GL2n
Xue, Hang
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2022, 74 (03): : 858 - 886
[2] Local Integrability of Characters on GL(2), Orbital Integrals, Germs
Flicker, Yuval Z.
JOURNAL OF LIE THEORY, 2017, 27 (01) : 123 - 137
[3] Representations of <mml:semantics>GLn(D)</mml:mrow><mml:annotation encoding="application/x-tex">$GL_n(D)$</mml:annotation></mml:semantics> near the identity
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PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2024, 129 (06)
[4] Relation of orbital integrals on SO(5) and PGL(2)
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Israel Journal of Mathematics, 1998, 106 : 29 - 77
[5] Invariant proper destributions on symmetric pairs (gl(4, R), gl (2, R) x gl (2, R))
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Jacquet, Nicolas
JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 261 (09) : 2362 - 2436
[6] FOURIER TRANSFORMS OF SEMISIMPLE ORBITAL INTEGRALS ON THE LIE ALGEBRA OF SL2
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PACIFIC JOURNAL OF MATHEMATICS, 2011, 254 (02) : 407 - 448
[7] Combinatorial Results on (1,2,1,2)-Avoiding GL(p, C) x GL(q, C)-Orbit Closures on GL(p plus q, C) / B
Woo, Alexander
Wyser, Benjamin J.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (24) : 13148 - 13193
[8] Arithmetic differential equations on GLn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GL_n$$\end{document}, II: arithmetic Lie–Cartan theory
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Taylor Dupuy
Selecta Mathematica, 2016, 22 (2) : 447 - 528
[9] Blocks with defect group Z2n x Z2n x Z2m
Wu, Chao
Zhang, Kun
Zhou, Yuanyang
JOURNAL OF ALGEBRA, 2018, 510 : 469 - 498
[10] Blocks with the hyperfocal subgroup Z2n X Z2n
Hu, Xueqin
Zhou, Yuanyang
JOURNAL OF ALGEBRA, 2019, 518 : 57 - 74

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