The DARK side of generalized Demazure crystals

Abstract

Naoi showed that tensor products of perfect Kirillov-Reshetikhin crystals are isomorphic to certain generalized Demazure crystals. We extend Naoi's results to address distinguished subsets of these tensor products. In type A, these are naturally described in terms of katabolizable tableaux which was key to resolving conjectures of Shimozono-Weyman and Chen-Haiman in arXiv:2007.04952.