Journal of Lie Theory 35 (2025), No. 3, 593--616
Copyright Heldermann Verlag 2025
Irreducible Characters of the Generalized Symmetric Group
Huimin Gao
School of Mathematics, Southern University of Science and Technology, Shenzhen, P.R.China
12431006@mail.sustech.edu.cn
Naihuan Jing
Department of Mathematics, North Carolina State University, Raleigh, U.S.A.
jing@ncsu.edu
[Abstract-pdf]
We study how to compute irreducible characters of the generalized symmetric group $C_k\wr{S}_n$ by iterative algorithms. After proving the Ariki-Koike version of the Murnaghan-Nakayama rule by vertex algebraic method, we formulate a new iterative formula for characters of the generalized symmetric group. As application we find a numerical relation between the character values of $C_k\wr S_n$ and modular characters of $S_{kn}$.
Keywords: Murnaghan-Nakayama rule, generalized symmetric groups, vertex operators.
MSC: 20C08, 05E10, 17B69.
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