Langlands duality for representations of quantum groups
نویسندگان
چکیده
منابع مشابه
Langlands Duality for Representations of Quantum Groups
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 bet...
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We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl n and sln, and give a complete reducibility result. These quantum groups have a natural n-dimensional module V . We prove an analogue of Schur-Weyl duality in this setting: the centralizer algebra of the quantum group action on the k-fold ten...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2010
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-010-0541-3