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

link: http://arxiv.org/abs/0902.0447
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. 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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