From conjugacy classes in the Weyl group to semisimple conjugacy classes

2019/03/11 by Jeffrey Adams, Adams, Jeffrey, Xuhua He +3
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1903.04089

Abstract

Suppose G is a connected complex semisimple group and W is its Weyl group. The lifting of an element of W to G is semisimple. This induces a well-defined map from the set of elliptic conjugacy classes of W to the set of semisimple conjugacy classes of G. In this paper, we give a uniform algorithm to compute this map. We also consider the twisted case.

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