Demazure modules and graded limits of minimal affinizations

Abstract

For a minimal affinization over a quantum loop algebra of type B C BC , we provide a character formula in terms of Demazure operators and multiplicities in terms of crystal bases. We also prove the formula for the limit of characters conjectured by Mukhin and Young. These are achieved by verifying that its graded limit (a variant of a classical limit) is isomorphic to some multiple generalization of a Demazure module, and by determining the defining relations of the graded limit.