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arXiv · 1512.09000

Convexity for twisted conjugation

Eckhard Meinrenken
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Abstract

Let $G$ be a compact, simply connected Lie group. If $\mathcal{C}_1,\mathcal{C}_2$ are two $G$-conjugacy classes, then the set of elements in $G$ that can be written as products $g=g_1g_2$ of elements $g_i\in \mathcal{C}_i$ is invariant under conjugation, and its image under the quotient map $G\to G/\operatorname{Ad}(G)$ is a convex polytope inside the Weyl alcove. In this note, we will prove an analogous statement for twisted conjugations relative to group automorphisms. The result will be obtained as a special case of a convexity theorem for group-valued moment maps which are equivariant with respect to the twisted conjugation action.

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Eckhard Meinrenken. 2015-12-30. Convexity for twisted conjugation. https://arxiv.org/abs/1512.09000

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