English

On the trace of Coxeter elements

Representation Theory 2024-11-28 v1

Abstract

Let W be a Weyl group and let w be a Coxeter elememt of minimal length of W. In the early 1970's I.G.Macdonald stated that the trace of w on an irreducible representation of W is 0,1 or -1. In this paper we give a proof of this statement and of an Iwahori-Hecke algebra version of it.

Keywords

Cite

@article{arxiv.2411.18495,
  title  = {On the trace of Coxeter elements},
  author = {G. Lusztig},
  journal= {arXiv preprint arXiv:2411.18495},
  year   = {2024}
}

Comments

10 pages

R2 v1 2026-06-28T20:14:49.330Z