Existence of Klyachko models for GL(n, R) and GL(n, C)

被引：6

作者：

Gourevitch, Dmitry ^{[2
]}

Offen, Omer ^{[3
]}

Sahi, Siddhartha ^{[4
]}

Sayag, Eitan ^{[1
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

[2] Weizmann Inst Sci, Fac Math & Comp Sci, IL-76100 Rehovot, Israel

[3] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[4] Rutgers State Univ, Dept Math, Hill Ctr, Piscataway, NJ 08854 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 08期

关键词：

Distinguished representations; Unitary dual; Highest derivatives; Mixed models; INVARIANT DISTRIBUTION VECTORS; GENERALIZED PRINCIPAL SERIES; REDUCTIVE SYMMETRICAL SPACES; UNITARY REPRESENTATIONS; RESIDUAL SPECTRUM; SYMPLECTIC GROUP; LINEAR-GROUPS; FIELD; CLASSIFICATION; CONJECTURE;

D O I：

10.1016/j.jfa.2012.01.023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that any irreducible unitary representation of GL(n, R) and GL(n, C) admits an equivariant linear form with respect to one of the subgroups considered by Klyachko. (c) 2012 Published by Elsevier Inc.

引用

页码：3585 / 3601

页数：17

共 36 条

[1] Aizenbud A, 2012, J LIE THEORY, V22, P137
[2] (GLn+1(F), GLn(F)) is a Gelfand pair for any local field F
Aizenbud, Avraham
Gourevitch, Dmitry
Sayag, Eitan
[J]. COMPOSITIO MATHEMATICA, 2008, 144 (06) : 1504 - 1524
[3] Aizenbud Avraham, MATH ACAD SCI PARIS, DOI [10.1016/j.crma.2011.11.011, DOI 10.1016/J.CRMA.2011.11.011]
[4] Avraham Aizenbud, ARXIV11094374
[5] A proof of Kirillov's conjecture
Baruch, EM
[J]. ANNALS OF MATHEMATICS, 2003, 158 (01) : 207 - 252
[6] BERNSTEIN IN, 1977, ANN SCI ECOLE NORM S, V10, P441
[7] BERNSTEIN JN, 1984, LECT NOTES MATH, V1041, P50
[8] H-INVARIANT DISTRIBUTION VECTORS FOR GENERALIZED PRINCIPAL SERIES OF REDUCTIVE SYMMETRICAL SPACES AND MEROMORPHIC EXTENTION OF EISENSTEIN INTEGRALS
BRYLINSKI, JL
DELORME, P
[J]. INVENTIONES MATHEMATICAE, 1992, 109 (03) : 619 - 664
[9] MEROMORPHIC BASIS OF H-INVARIANT DISTRIBUTION VECTORS FOR THE GENERALIZED PRINCIPAL SERIES OF REDUCTIVE SYMMETRICAL SPACES - FUNCTIONAL-EQUATION
CARMONA, J
DELORME, P
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (01) : 152 - 221
[10] Flath D., 1979, Automorphic forms, representations and L-functions, VXXXIII, P179

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