The Murnaghan-Nakayama rule and some virtual S_n characters

TL;DR

This paper develops a formula for calculating the values of specific virtual characters of symmetric groups, enhancing understanding of their representation theory.

Contribution

It introduces a new method to compute virtual characters of symmetric groups, expanding the tools available for algebraic and combinatorial analysis.

Findings

Derived explicit formulas for virtual character values

Enhanced computational techniques for symmetric group representations

Provided new insights into the structure of virtual characters

Abstract

We construct certain virtual characters for the symmetric groups, then compute a formula which calculates the values of these virtual characters.