Graded limits of minimal affinizations over the quantum loop algebra of type $G_2$

Abstract

The aim of this paper is to study the graded limits of minimal affinizations over the quantum loop algebra of type $G_2$. We show that the graded limits are isomorphic to multiple generalizations of Demazure modules, and obtain defining relations of them. As an application, we obtain a polyhedral multiplicity formula for the decomposition of minimal affinizations of type $G_2$ as a $U_q(\mathfrak{g})$-module, by showing the corresponding formula for the graded limits.

References in corpus (2)

• On minimal affinizations of representations of quantum groups
• Graded Limits of Minimal Affinizations in Type D

Cited by in corpus (1)

• Non-Minimality of Certain Irregular Coherent Preminimal Affinizations