A Note on Skew Characters of Symmetric Groups

TL;DR

This paper provides a new proof for a character value of the symmetric group, originally computed using Lie superalgebra representation theory, by employing skew characters instead.

Contribution

It introduces a novel proof technique for Regev's symmetric group character result using skew characters, offering an alternative approach.

Findings

New proof of Regev's character value using skew characters

Simplifies understanding of symmetric group characters

Connects representation theory of Lie superalgebras with skew characters

Abstract

In previous work Regev used part of the representation theory of Lie superalgebras to compute the values of a character of the symmetric group whose decomposition into irreducible constituents is described by semistandard $(k,\ell)$-tableaux. In this short note we give a new proof of Regev's result using skew characters.