Langlands duality for quantum affine algebras and simple tensor products.
-- David Hernandez (Ecole Polytechnique) --
In this talk, we will first discuss results obtained in collaboration with Edward Frenkel : we establish a correspondence (or duality) between representations of quantum (affine) algebras associated to Langlands dual complex Lie algebras. To prove the duality at the level of quantum affine algebras, we construct (q,t)-characters", depending on two parameters and interpolating between Frenkel-Reshetikhin q-characters attached to a quantum affine algebra and its Langlands dual.
In the second part of this talk, we will explain how in this Langlands duality framework we can use the recent proof by the speaker of the following conjecture : a tensor product of N simple finite
dimensional representations of a quantum affine algebra is simple if and only if the tensor products of the representations are simple two by two.

Edward Frenkel, lauréat de la Chaire d’Excellence 2008 de la Fondation, propose pour clôturer sa Chaire une journée de conférences le jeudi 17 juin 2010 à l’IHP (Amphithéâtre Hermite), sur le thème Symmetry, Duality, and Cinema

Cette journée a proposé des exposés d’Edward Frenkel mais aussi de David Hernandez (Ecole Polytechnique), Vincent Lafforgue (IMJ) et Nikita Nekrasov (IHES).