On minimal affinizations of representations of quantum groups

Details On minimal affinizations of representations of quantum groups On minimal affinizations of representations of quantum groups

2006-07-21

arxiv.org/abs/math/0607527v4

Commun.Math.Phys.277:221-259,2007

Mathematics

Quantum Algebra

38 pages; references and additional results added. Accepted for publication in Communications in Mathematical Physics

Scientific paper

10.1007/s00220-007-0332-1

In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced by Chari). 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 affinization in types C, D, F. As an application, the Frenkel-Mukhin algorithm 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 Nakai-Nakanishi (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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