Crystals for Kostant-Kumar modules of $\widehat{{\mathfrak{sl}}_2}$

Abstract

We consider the affine Lie algebra $\widehat{{\mathfrak{sl}}_2}$ and the Kostant-Kumar submodules of tensor products of its level 1 highest weight integrable representations. We construct crystals for these submodules in terms of the charged partitions model and describe their decomposition into irreducibles.

26 pages