1School of Mathematics, Southern University of Science and Technology, Shenzhen, P.R.China 2Department of Mathematics, North Carolina State University, Raleigh, U.S.A.
Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 593-616
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 $S_{kn}$.
1
School of Mathematics, Southern University of Science and Technology, Shenzhen, P.R.China
2
Department of Mathematics, North Carolina State University, Raleigh, U.S.A.
Huimin Gao; Naihuan Jing. Irreducible Characters of the Generalized Symmetric Group. Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 593-616. http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a7/
@article{JOLT_2025_35_3_a7,
author = {Huimin Gao and Naihuan Jing},
title = {Irreducible {Characters} of the {Generalized} {Symmetric} {Group}},
journal = {Journal of Lie Theory},
pages = {593--616},
year = {2025},
volume = {35},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a7/}
}
TY - JOUR
AU - Huimin Gao
AU - Naihuan Jing
TI - Irreducible Characters of the Generalized Symmetric Group
JO - Journal of Lie Theory
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