Graded limits of minimal affinizations over the quantum loop algebra of type $G_2$
arXiv:1503.02178 · doi:10.1007/s10468-016-9606-7
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.