Journal of Lie Theory

no. 3
Irreducible Characters of the Generalized Symmetric Group
Journal of Lie Theory, Volume 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 $S_{kn}$.
DOI: 10.5802/jolt.1399
Classification: 20C08, 05E10, 17B69
Keywords: Murnaghan-Nakayama rule, generalized symmetric groups, vertex operators 
@article{JOLT_2025_35_3_a7,
     author = {H. Gao and N. Jing},
     title = {Irreducible {Characters} of the {Generalized} {Symmetric} {Group}},
     journal = {Journal of Lie Theory},
     pages = {593--616},
     year = {2025},
     volume = {35},
     number = {3},
     doi = {10.5802/jolt.1399},
     zbl = {08103104},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1399/}
}
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H. Gao; N. Jing. Irreducible Characters of the Generalized Symmetric Group. Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 593-616. doi: 10.5802/jolt.1399

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