From conjugacy classes in the Weyl group to semisimple conjugacy classes

Jeffrey Adams; Xuhua He; Sian Nie

From conjugacy classes in the Weyl group to semisimple conjugacy classes

Representation Theory 2020-03-31 v2

Authors: Jeffrey Adams , Xuhua He , Sian Nie

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.

Keywords

connected complex semisimple group weyl group elliptic conjugacy class semisimple conjugacy class lifting map uniform algorithm twisted case

Cite

@article{arxiv.1903.04089,
  title  = {From conjugacy classes in the Weyl group to semisimple conjugacy classes},
  author = {Jeffrey Adams and Xuhua He and Sian Nie},
  journal= {arXiv preprint arXiv:1903.04089},
  year   = {2020}
}

Comments

28 pages. Final version. To appear in PAMQ

From conjugacy classes in the Weyl group to semisimple conjugacy classes

Abstract

Keywords

Cite

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