Multiplicity free expansions of Schur $P$-functions

TL;DR

This paper investigates conditions under which Schur P-functions expand into Schur functions without multiplicities and explores related multiplicity phenomena in spin characters of twisted symmetric groups.

Contribution

It provides new criteria for multiplicity free expansions of Schur P-functions and analyzes multiplicities in spin character products of twisted symmetric groups.

Findings

Criteria for multiplicity free Schur P-function expansions

Conditions for multiplicity free products of spin characters

Characterization of multiplicities in twisted symmetric group representations

Abstract

After deriving inequalities on coefficients arising in the expansion of a Schur $P$-function in terms of Schur functions we give criteria for when such expansions are multiplicity free. From here we study the multiplicity of an irreducible spin character of the twisted symmetric group in the product of a basic spin character with an irreducible character of the symmetric group, and determine when it is multiplicity free.