Langlands duality for finite-dimensional representations of quantum affine algebras

Abstract

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the Kirillov-Reshetikhin modules and their irreducible tensor products. In the course of the proof we introduce and construct "interpolating (q,t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.

40 pages; several results and comments added. Accepted for publication in Letters in Mathematical Physics

References in corpus (4)

• Cluster algebras and quantum affine algebras
• On minimal affinizations of representations of quantum groups
• Simple tensor products
• Langlands duality for representations and quantum groups at a root of unity

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