Generating Functions for Hecke Algebra Characters

Generating Functions for Hecke Algebra Characters

Certain polynomials in n variables which serve as generating functions for symmetric group characters are sometimes called (Sn) character immanants. We point out a close connection between the identities of Littlewood-Merris-Watkins and Goulden-Jackson, which relate Sn character immanants to the determinant, the permanent and MacMahon’s Master Theorem. From these results we obtain a generalizat...

Hecke Algebra Characters

Hecke algebra characters and quantum chromatic symmetric functions

We evaluate induced sign characters of Hn(q) at certain elements of Hn(q) and conjecture an interpretation for the resulting polynomials as generating functions for P -tableaux by a certain statistic. Our conjecture relates the quantum chromatic symmetric functions of Shareshian and Wachs to Hn(q) characters. Résumé. Nous évaluons les caractères de signe induits de Hn(q) à certains éléments de ...

Hecke Algebra Characters and Immanant Conjectures

The main purpose of this article is to announce and provide supporting evidence for two conjectures about the characters of the Hecke algebra Hn(q) of type An_I' evaluated at elements of its Kazhdan-Lusztig basis. In addition, we prove a conjectured immanant inequality for Jacobi-Trudi matrices (definitions below) and show how our conjectures would imply stronger inequalities of a similar kind....

On Permutation Statistics and Hecke Algebra Characters

Irreducible characters of Hecke algebras of type A may be represented as reened 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 g...