The character values of Iwahori--Hecke algebras on Coxeter basis elements

TL;DR

This paper provides explicit tables of character values of Iwahori--Hecke algebras on Coxeter basis elements, complementing Lusztig's work on traces of Coxeter elements, with proofs based on Lusztig's theory of Coxeter orbits and Frobenius eigenspaces.

Contribution

It offers explicit character value tables for Iwahori--Hecke algebras on Coxeter basis elements, expanding understanding of their trace properties.

Findings

Explicit tables for traces of Coxeter basis elements

Connection with Lusztig's Coxeter orbits and Frobenius eigenspaces

Complementary to Lusztig's recent work

Abstract

These are unpublished notes from about 1992-1993 which, retrospectively, may be regarded as a complement to Lusztig's recent paper on the trace of Coxeter elements. Our notes include explicit tables for those traces. The proofs rely on a connection with Lusztig's work on Coxeter orbits and eigenspaces of Frobenius, which may be of independent interest.