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arXiv · 2312.13681

Irreducible characters and bitrace for the $q$-rook monoid

Naihuan Jing·Yu Wu·Ning Liu
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Abstract

This paper studies irreducible characters of the $q$-rook monoid algebra $R_n(q)$ using the vertex algebraic method. Based on the Frobenius formula for $R_n(q)$, a new iterative character formula is derived with the help of the vertex operator realization of the Schur symmetric function. The same idea also leads to a simple proof of the Murnaghan-Nakayama rule for $R_n(q)$. We also introduce the bitrace for the $q$-rook monoid and derive its combinatorial formula as a generalization of the bitrace formula for the Iwahori-Hecke algebra. The character table of $R_n(q)$ with $|\mu|=5$ is listed in the appendix.

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BibTeXRIS

Naihuan Jing, Yu Wu, Ning Liu. 2023-12-21. Irreducible characters and bitrace for the $q$-rook monoid. https://doi.org/10.1080/00927872.2025.2554338

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