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On Minimal Affinizations of Representations of Quantum Groups

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In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced in [Cha1]). We prove that all minimal affinizations in types A, B, G are special in the sense of monomials. Although this property is not satisfied in general, we also prove an analog property for a large class of minimal affinizations in types C, D, F. As an application, the Frenkel-Mukhin algorithm [FM1] works for these modules. For minimal affinizations of type A, B we prove the thin property (the l-weight spaces are of dimension 1) and a conjecture of [NN1] (already known for type A). The proof of the special property is extended uniformly for more general quantum affinizations of quantum Kac-Moody algebras.

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Hernandez, D. On Minimal Affinizations of Representations of Quantum Groups. Commun. Math. Phys. 276, 221–259 (2007). https://doi.org/10.1007/s00220-007-0332-1

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