Crystals and Schur $P$-positive expansions

TL;DR

This paper introduces a new crystal-theoretic characterization of Littlewood-Richardson-Stembridge tableaux for Schur P-functions and provides alternative proofs for key Schur P-expansion formulas using crystal structures.

Contribution

It offers a novel crystal-based characterization of tableaux related to Schur P-functions and re-proves important expansion formulas through crystal theory.

Findings

New crystal characterization of Littlewood-Richardson-Stembridge tableaux

Alternative proofs of Schur P-expansion formulas

Enhanced understanding of Schur P-function expansions

Abstract

We give a new characterization of Littlewood-Richardson-Stembridge tableaux for Schur $P$-functions by using the theory of $\mf{q}(n)$-crystals. We also give alternate proofs of the Schur $P$-expansion of a skew Schur function due to Ardila and Serrano, and the Schur expansion of a Schur $P$-function due to Stembridge using the associated crystal structures.