English

On certain varieties attached to braid representatives of a Weyl group element

Representation Theory 2023-12-11 v1

Abstract

Let GG be a connected reductive group over an algebraically closed field with Weyl group WW. The analogy between Lusztig varieties and Deligne-Lusztig varieties associated to minimal length elements in elliptic conjugacy classes of WW was studied by He and Lusztig. In this paper, we study the parabolic version of above varieties associated to some good braid elements for any conjugacy class of WW. This also leads to an alternative version of Lusztig's map in general case.

Keywords

Cite

@article{arxiv.2312.04798,
  title  = {On certain varieties attached to braid representatives of a Weyl group element},
  author = {Chengze Duan},
  journal= {arXiv preprint arXiv:2312.04798},
  year   = {2023}
}