A super Frobenius formula for the characters of Iwahori-Hecke algebras

TL;DR

This paper introduces a super Frobenius formula linking Hall-Littlewood supersymmetric functions to the characters of Iwahori-Hecke algebras, unifying quantum and classical super cases.

Contribution

It establishes a new super Frobenius formula that connects supersymmetric functions with algebra characters, extending previous classical and quantum results.

Findings

Hall-Littlewood supersymmetric functions generate character values

The formula applies to both quantum and classical super cases

Provides a unified framework for Iwahori-Hecke algebra characters

Abstract

We establish a super Frobenius formula for the characters of Iwahori-Hecke algebras. We show that the Hall-Littlewood sypersymmetric function, up to constant, generates the values of the irreducible characters of Iwahori-Hecke algebras at the elements corresponding to cycle permutations. Our formula in this article includes both the ordinary quantum case and the classical super case.