On Minimal Affinizations of Representations of Quantum Groups

By D. Hernandez. 2006

65 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/289142fdcc130a6e3b0253f89500d48d6e2c4d9a

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

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Citations in the corpus

Simple tensor products (2009, unknown): “The proof of the following duality result can be found in [ 17 ] for the untwisted types (the highest weight term is computed in [9]).”
Quantum toroidal algebras and their representations (2008, background): “Many combinatorial results and explicit formulas are known forq-characters of Kirillov{Reshetikhin modules, in particular for quantum ane algebras of classical types (see references in [ He6 ]).”