Polar representations of compact groups and convex hulls of their orbits

被引：8

作者：

Gichev, V. M. ^{[1
]}

机构：

[1] Sobolev Inst Math, Omsk Branch, Omsk 644099, Russia

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2010年 / 28卷 / 05期

关键词：

Polar representations; Semigroups of sets; Coxeter groups;

D O I：

10.1016/j.difgeo.2010.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper contains a characterization of compact groups G subset of GL(0), where o is a finite-dimensional real vector space, which have the following property SP: the family of convex hulls of G-orbits is a semigroup with respect to the Minkowski addition. If G is finite, then SP holds if and only if G is a Coxeter group; if G is connected then SP is equivalent to the property to be polar. In general, G satisfies SP if and only if it is polar and its Weyl group is a Coxeter group. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：608 / 614

页数：7

共 14 条

[1] Geometric groups. I [J].