Lie superalgebras and some characters of $S_n$

TL;DR

This paper derives a formula for characters of the symmetric group $S_n$ associated with partitions in the $(k, ext{ell})$ hook, utilizing combinatorial aspects of Lie superalgebra theory.

Contribution

It introduces a novel combinatorial approach to compute $S_n$ characters linked to specific partitions via Lie superalgebra methods.

Findings

Derived a new character formula for $S_n$ partitions in the $(k, ext{ell})$ hook.

Applied Lie superalgebra theory to combinatorial problems in symmetric group representations.

Enhanced understanding of the interplay between Lie superalgebras and symmetric group characters.

Abstract

We prove a formula for $S_n$ characters which are indexed by the partitions in the $(k,\ell)$ hook. The proof applies a combinatorial part of the theory of Lie superalgebras.