On Permutation Statistics and Hecke Algebra Characters

Abstract

Irreducible characters of Hecke algebras of type $A$ may be represented as refined counts of simple statistics on suitable subsets of permutations. Such formulas have been generalized to characters of other Coxeter groups and their Hecke algebras and to coinvariant algebras. In this paper we present several formulas, applications to combinatorial identities, and related problems. New results are given with proofs.