Langlands duality for finite-dimensional representations of quantum affine algebras

Details Langlands duality for finite-dimensional representations of quantum affine algebras Langlands duality for finite-dimensional representations of quantum affine algebras

2009-02-03

arxiv.org/abs/0902.0447v4

Lett.Math.Phys.96:217-261,2011

Mathematics

Quantum Algebra

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

Scientific paper

10.1007/s11005-010-0426-0

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.

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