On characters of wreath products

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, 05E10Keywords: Character identity, wreath product, partition, Murnaghan-Nakayama rule, colored permutations