Polar representations of compact groups and convex hulls of their orbits

Details Polar representations of compact groups and convex hulls of their orbits Polar representations of compact groups and convex hulls of their orbits

2009-09-02

arxiv.org/abs/0909.0379v1

Differential Geometry and its Applications, 28 (2010), 608-614

Mathematics

Metric Geometry

Scientific paper

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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