Axioms for Shifted Tableau Crystals

Abstract

We give local axioms that uniquely characterize the crystal-like structure on shifted tableaux developed by the authors and Purbhoo. These axioms closely resemble those developed by Stembridge for type A tableau crystals. This axiomatic characterization gives rise to a new method for proving and understanding Schur $Q$-positive expansions in symmetric function theory, just as the Stembridge axiomatic structure provides for ordinary Schur positivity.