Polar orthogonal representations of real reductive algebraic groups

被引：4

作者：

Geatti, Laura ^{[2
]}

Gorodski, Claudio ^{[1
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, Brazil

[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

来源：

JOURNAL OF ALGEBRA | 2008年 / 320卷 / 07期

关键词：

polar representations; real reductive algebraic groups; pseudo-Riemannian symmetric spaces;

D O I：

10.1016/j.jalgebra.2008.06.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：3036 / 3061

页数：26

共 50 条

[21] EQUIVARIANT ALGEBRAIC VECTOR-BUNDLES OVER REPRESENTATIONS OF REDUCTIVE GROUPS - APPLICATIONS
MASUDA, M
MOSERJAUSLIN, L
PETRIE, T
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1991, 88 (20) : 9065 - 9066
[22] EQUIVARIANT ALGEBRAIC VECTOR-BUNDLES OVER REPRESENTATIONS OF REDUCTIVE GROUPS - THEORY
MASUDA, M
PETRIE, T
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1991, 88 (20) : 9061 - 9064
[23] Abstract irreducible representations of reductive algebraic groups with Borel-stable line
Chen, Xiaoyu
SELECTA MATHEMATICA-NEW SERIES, 2024, 30 (05):
[24] On covariants of reductive algebraic groups
Panyushev, DI
INDAGATIONES MATHEMATICAE-NEW SERIES, 2002, 13 (01): : 125 - 129
[25] REAL REPRESENTATIONS OF THE FINITE ORTHOGONAL AND SYMPLECTIC GROUPS OF ODD CHARACTERISTIC
GOW, R
JOURNAL OF ALGEBRA, 1985, 96 (01) : 249 - 274
[26] CONTINUOUS CO-HOMOLOGY AND UNITARY REPRESENTATIONS OF REAL REDUCTIVE GROUPS
ZUCKERMAN, GJ
ANNALS OF MATHEMATICS, 1978, 107 (03) : 495 - 516
[27] Topology of moduli spaces of free group representations in real reductive groups
Casimiro, Ana
Florentino, Carlos
Lawton, Sean
Oliveira, Andre
FORUM MATHEMATICUM, 2016, 28 (02) : 275 - 294
[28] WEIGHT FILTRATIONS FOR INDUCED REPRESENTATIONS OF REAL REDUCTIVE LIE-GROUPS
CASIAN, LG
COLLINGWOOD, DH
ADVANCES IN MATHEMATICS, 1989, 73 (01) : 79 - 146
[29] On the nullcone of representations of reductive groups
Kraft, H
Wallach, NR
PACIFIC JOURNAL OF MATHEMATICS, 2006, 224 (01) : 119 - 139
[30] Representations of Abelian algebraic groups
Langlands, RP
PACIFIC JOURNAL OF MATHEMATICS, 1997, : 231 - 250

← 1 2 3 4 5 →