English

Hecke modules based on involutions in extended Weyl groups

Representation Theory 2017-10-11 v1

Abstract

Let X be the group of weights of a maximal torus of a simply connected semisimple group over C and let W be the Weyl group. The semidirect product W(Q\otimes X/X) is called the extended Weyl group. There is a natural C(v)-algebra H called the extended Hecke algebra with basis indexed by the extended Weyl group which contains the usual Hecke algebra as a subalgebra. We construct an H-module with basis indexed by the involutions in the extended Weyl group. This generalizes a construction of the author and D.Vogan.

Keywords

Cite

@article{arxiv.1710.03670,
  title  = {Hecke modules based on involutions in extended Weyl groups},
  author = {G. Lusztig},
  journal= {arXiv preprint arXiv:1710.03670},
  year   = {2017}
}

Comments

38 pages

R2 v1 2026-06-22T22:09:01.731Z