Restricted limits of minimal affinizations

TL;DR

This paper derives character formulas for minimal affinizations of quantum group representations in orthogonal types, especially for weights supported on limited Dynkin diagram nodes, and extends techniques to broader cases.

Contribution

It introduces new character formulas for minimal affinizations in orthogonal Lie algebras and provides a framework for generalization, including a proof of a conjecture in type D4.

Findings

Character formulas for minimal affinizations in orthogonal types.

A framework for extending techniques to more general cases.

Proof of a conjecture of Chari and Pressley in type D4.

Abstract

We obtain character formulas of minimal affinizations of representations of quantum groups when the underlying simple Lie algebra is orthogonal and the support of the highest weight is contained in the first three nodes of the Dynkin diagram. We also give a framework for extending our techniques to a more general situation. In particular, for the orthogonal algebras and a highest weight supported in at most one spin node, we realize the restricted classical limit of the corresponding minimal affinizations as a quotient of a module given by generators and relations and, furthermore, show that it projects onto the submodule generated by the top weight space of the tensor product of appropriate restricted Kirillov-Reshetikhin modules. We also prove a conjecture of Chari and Pressley regarding the equivalence of certain minimal affinizations in type D4.