Langlands duality for finite-dimensional representations of quantum affine algebras

Edward Frenkel , David Hernandez (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Algèbres quantiques [math.QA]; Théorie des représentations [math.RT]

Edward Frenkel, David Hernandez. Langlands duality for finite-dimensional representations of quantum affine algebras. 2009. ⟨hal-00358632⟩