Polar representations of compact groups and convex hulls of their orbits

V. Gichev

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arXiv · 0909.0379

Polar representations of compact groups and convex hulls of their orbits

V. Gichev

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Abstract

The paper contains a characterization of compact groups $G\subseteq\GL(V)$, where $V$ 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 true if and only if $G$ is polar. In general, $G$ satisfies \SP{} if and only if it is polar and its Weyl group is a Coxeter group.

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BibTeX RIS

V. Gichev. 2009-09-02. Polar representations of compact groups and convex hulls of their orbits. https://arxiv.org/abs/0909.0379

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