T-duality for Langlands dual 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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By normalizing a component of the space of commuting pairs of elements in a reductive Lie group G, and the corresponding space for the Langlands dual group, we construct pairs of hyperkähler orbifolds which satisfy the conditions to be mirror partners in the sense of Strominger-Yau-Zaslow. The same holds true for commuting quadruples in a compact Lie group. The Hodge numbers of the mirror partn...
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The category of perverse sheaves on the affine Grassmannian of a complex reductive group G gives a canonical geometric construction of the split form of the Langlands dual group ǦZ over the integers [6]. Given a field k, we give a Tannakian construction of the quasi-split forms of Ǧk, as well as a construction of the gerbe associated to an inner form of Ǧk.
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In the late 1960s Robert Langlands launched what has become known as the Langlands Program with the ambitious goal of relating deep questions in Number Theory to Harmonic Analysis [L]. In particular, Langlands conjectured that Galois representations and motives can be described in terms of the more tangible data of automorphic representations. A striking application of this general principle is...
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We show that the numerical local Langlands duality for GLn and the T-duality of twodimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local Fourier transform in both its `-adic and complex incarnation gives rise to symmetries of arithmetic and geometric local Langlands parameters.
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ژورنال
عنوان ژورنال: Advances in Theoretical and Mathematical Physics
سال: 2014
ISSN: 1095-0761,1095-0753
DOI: 10.4310/atmp.2014.v18.n6.a2