Graded Limits of Minimal Affinizations over the Quantum Loop Algebra of Type G2

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 -module, by showing the corresponding formula for the graded limits. As another application, we prove a character formula of the least affinizations of generic parabolic Verma modules of type G (2) conjectured by Mukhin and Young.