Langlands duality for representations of quantum groups |
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Authors: | Edward Frenkel David Hernandez |
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Institution: | 1.Department of Mathematics,University of California,Berkeley,USA;2.CNRS, école Normale Supérieure, DMA,Paris,France |
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Abstract: | 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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