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.
