On characters of wreath products
Ron M. Adin, Yuval Roichman

TL;DR
This paper provides a concise combinatorial proof of a character identity relating hyperoctahedral and symmetric groups, and extends it to other wreath products, offering a new perspective beyond algebraic and Lie theoretic methods.
Contribution
It introduces a short combinatorial proof of a known character identity and generalizes it to a broader class of wreath products.
Findings
Combinatorial proof of the character identity for $B_n$ and $S_{2n}$
Extension of the identity to other wreath products
Simplification of the proof method compared to algebraic approaches
Abstract
A character identity which relates irreducible character values of the hyperoctahedral group to those of the symmetric group was recently proved by L\"ubeck 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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Advanced Algebra and Geometry
