English

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.

Keywords

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