The sections of the Weyl group
Representation Theory
2021-03-18 v2 Group Theory
Number Theory
Abstract
We compute all sections of the finite Weyl group, that satisfy the braid relations, in the case that G is an almost-simple connected reductive group defined over an algebraically closed field. We then demonstrate that this set of sections has an interesting partially ordered structure, and also give some applications.
Cite
@article{arxiv.1912.07665,
title = {The sections of the Weyl group},
author = {Moshe Adrian},
journal= {arXiv preprint arXiv:1912.07665},
year = {2021}
}
Comments
23 pages, to appear in IMRN. In addition to computing the sections of the Weyl group, in this version we now also classify all T-conjugacy classes of sections. Fixed typo in the computations for type D_n adjoint, fixed mistake in the computations for type B_n adjoint. Fixed definition of partial order