English

Irreducible characters of the generalized symmetric group

Representation Theory 2025-12-02 v2 Combinatorics Group Theory

Abstract

The paper studies how to compute irreducible characters of the generalized symmetric group CkSnC_k\wr{S}_n by iterative algorithms. After reproving the Ariki-Koike version of the Murnaghan-Nakayama rule by vertex algebraic methods, we formulate a new iterative formula for characters of the generalized symmetric group. As applications, we find a numerical relation between the character values of CkSnC_k\wr S_n and modular characters of SknS_{kn}.

Keywords

Cite

@article{arxiv.2408.04921,
  title  = {Irreducible characters of the generalized symmetric group},
  author = {Huimin Gao and Naihuan Jing},
  journal= {arXiv preprint arXiv:2408.04921},
  year   = {2025}
}

Comments

24 pages; code appended. Updated references