Irreducible characters and bitrace for the q-rook monoid

2023/12/21 by Naihuan Jing, Jing, Naihuan, Yu Jing Wu +3 · 1 citation
Computer Science · Mathematics · #05E10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Primary: 20C08 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary: 17B69

paper · pdf · doi:10.48550/arxiv.2312.13681

openalex publication_date 2023/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 |μ|=5 is listed in the appendix.

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