Dual Murnaghan-Nakayama rule for Hecke algebras in Type $A$

Abstract

Let ${\chi }_{\mu }^{\lambda }$ be the value of the irreducible character ${\chi }^{\lambda }$ of the Hecke algebra of the symmetric group on the conjugacy class of type $\mu$. The usual Murnaghan-Nakayama rule provides an iterative algorithm based on reduction of the lower partition $\mu$. In this paper, we establish a dual Murnaghan-Nakayama rule for Hecke algebras of type $A$ using vertex operators by applying reduction to the upper partition $\lambda$. We formulate an explicit recursion of the dual Murnaghan-Nakayama rule by employing the combinatorial model of ``brick tabloids", which refines a previous result by two of us (J. Algebra 598 (2022), 24--47).

11pp; Authors are ordered according to the standard practice