Restricted limits of minimal affinizations

Details Restricted limits of minimal affinizations Restricted limits of minimal affinizations

2008-12-11

arxiv.org/abs/0812.2238v2

Pacific J. Math 244 (2010), no. 2, 359-397

Mathematics

Representation Theory

Referee's suggestions added. Several minor typos, corrections, and improvements made

Scientific paper

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.

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