Stanley character formula for the spin characters of the symmetric groups

TL;DR

This paper introduces a new formula for calculating irreducible spin characters of symmetric groups, extending Stanley's character formula from linear to spin representations, providing a novel computational tool.

Contribution

The paper presents a novel formula for spin characters of symmetric groups, analogous to Stanley's formula for linear characters, advancing the understanding of spin representation theory.

Findings

Derived a new formula for spin characters

Established analogy with Stanley's formula for linear characters

Provides a computational method for spin representations

Abstract

We give a new formula for the irreducible spin characters of the symmetric groups. This formula is analogous to Stanley's character formula for the usual (linear) characters of the symmetric groups.