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Langlands duality for representations of quantum groups

Hernandez, D (CNRS-ENS Paris)
Tuesday 24 March 2009, 16:30-17:30

Seminar Room 1, Newton Institute


This is a joint work with E. Frenkel. We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in terms of semi-simple Lie algebras. To explain this duality, we introduce an "interpolating quantum group" depending on two parameters which interpolates between a quantum group and its Langlands dual. We construct examples of its representations, depending on two parameters, which interpolate between representations of two Langlands dual quantum groups.


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