Demazure modules and graded limits of minimal affinizations

Abstract

For a minimal affinization over a quantum loop algebra of type 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.

Graded Limits of Minimal Affinizations over the Quantum Loop Algebra of Type G 2

“…First we introduce the following notation, as in [Nao13,Nao14]. Assume that V is a g-module and D is a b-submodule of V .…”

“…Graded limits of minimal affinizations, which are graded analogs of the classical limits defined over the current algebra g[t] = g ⊗ C[t], were studied in [Cha01], [CM06], [Mou10], [MP11], [Nao13], [Nao14].…”

Graded Limits of Simple Tensor Product of Kirillov–Reshetikhin Modules for

“…In this article, we consider the following generalization of Demazure modules introduced in [30]. Given m ∈ Z ≥1 and pairs w r…”

“…The graded limits of general minimal affinizations were first studied in [26] a set of defining relations for them were conjectured. Using the theory of Demazure modules, the conjecture was established in [30,31] for of classical type and in [24] for type G 2 . It was also partially established for type E 6 in [27].…”

On the extended T-system of type $$C_3$$ C 3

“…Minimal affinizations are studied intensively in recently years, see for example, [CMY12], [CG11], [Her07], [LM12], [Mou10], [MF11], [MY12a], [MY12b], [MY12c], [Nao12]. The finite dimensional representations of U qĝ and cluster algebras are closely related, see [IIKKN13a], [IIKKN13b], [HL10], [HL13], [Nak11].…”