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arXiv · 2503.12299

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

Naihuan Jing·Ning Liu·Yu Wu
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Abstract

Let $\chi^{\lambda}_{\mu}$ 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).

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BibTeXRIS

Naihuan Jing, Ning Liu, Yu Wu. 2025-03-16. Dual Murnaghan-Nakayama rule for Hecke algebras in Type $A$. https://arxiv.org/abs/2503.12299

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