On combinatorial formulas for the characters of Hecke algebras

TL;DR

This paper develops combinatorial formulas for characters of Hecke algebras, extending known results in type A to types B and C, and providing complete descriptions for type I.

Contribution

It introduces combinatorial proofs for character formulas of Hecke algebras, generalizing results across multiple types and including new descriptions for type I.

Findings

Combinatorial formulas for Hecke algebra characters in types B and C.

Generalization of type A results to other types.

Complete character descriptions for type I.

Abstract

Hecke algebras are beautiful q-extensions of Coxeter groups. In this paper, we prove several results on their characters, with an emphasis on characters induced from trivial and sign representations of parabolic subalgebras. While most of the results in type A are known, our proofs are of a combinatorial nature, and generalize to (partial) results in types B and C. We also present complete descriptions of such characters for type I.