Irreducible Characters of the Generalized Symmetric Group
Copyright policy )Irreducible Characters of the Generalized Symmetric Group
The paper studies how to compute irreducible characters of the generalized symmetric group $C_k\wr{S}_n$ 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 $C_k\wr S_n$ and modular characters of $S_{kn}$.
24 pages; code appended. Updated references
Representation Theory, Combinatorics, Group Theory, FOS: Mathematics, Combinatorics (math.CO), Group Theory (math.GR), Representation Theory (math.RT), Primary: 20C08, Secondary: 05E10, 17B69
Representation Theory, Combinatorics, Group Theory, FOS: Mathematics, Combinatorics (math.CO), Group Theory (math.GR), Representation Theory (math.RT), Primary: 20C08, Secondary: 05E10, 17B69
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