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arXiv · 2104.06067

On irreducible characters of the Iwahori-Hecke algebra in type $A$

Naihuan Jing·Ning Liu
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Abstract

We use vertex operators to compute irreducible characters of the Iwahori-Hecke algebra of type $A$. Two general formulas are given for the irreducible characters in terms of those of the symmetric groups or the Iwahori-Hecke algebras in lower degrees. Explicit formulas are derived for the irreducible characters labeled by hooks and two-row partitions. Using duality, we also formulate a determinant type Murnaghan-Nakayama formula and give another proof of Ram's combinatorial Murnaghan-Nakayama formula. As applications, we study super-characters of the Iwahori-Hecke algebra as well as the bitrace of the regular representation and provide a simple proof of the Halverson-Luduc-Ram formula.

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BibTeXRIS

Naihuan Jing, Ning Liu. 2021-04-13. On irreducible characters of the Iwahori-Hecke algebra in type $A$. https://doi.org/10.1016/j.jalgebra.2022.01.020

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