Unlocking Langlands Duality in Quantum Affine Algebras & Tensor Products 🔑

Langlands duality for quantum affine algebras and simple tensor products.<br />-- David Hernandez (Ecole Polytechnique) --<br />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.<br />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<br />dimensional representations of a quantum affine algebra is simple if and only if the tensor products of the representations are simple two by two.<br /><br />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<br /><br />Cette journée a proposé des exposés d’Edward Frenkel mais aussi de David Hernandez (Ecole Polytechnique), Vincent Lafforgue (IMJ) et Nikita Nekrasov (IHES).