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On characters of wreath products
Abstract
A character identity which relates irreducible character values of the hyperoctahedral group \(B_n\) to those of the symmetric group \(S_{2n}\) was recently proved by Lübeck and Prasad. Their proof is algebraic and involves Lie theory. We present a short combinatorial proof of this identity, as well as a generalization to other wreath products.
Mathematics Subject Classifications: 20C30, 20E22, 05E10
Keywords: Character identity, wreath product, partition, Murnaghan-Nakayama rule, colored permutations