A local characterization of $B_2$ regular crystals

Abstract

Stembridge characterized regular crystals associated with a simply-laced generalized Cartan matrix (GCM) in terms of local graph-theoretic quantities. We give a similar axiomatization for $B_2$ regular crystals and thus for regular crystals associated with a finite GCM except $G_2$ and an affine GCM except $A_1^{(1)},G_2^{(1)},A_2^{(2)},D_4^{(3)}$.

15 pages, submitted to a journal as a revision in October 2019