Twisted Whittaker model and factorizable sheaves

2007/05/31 by Dennis Gaitsgory, Gaitsgory, Dennis
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.0705.4571

Abstract

Let G be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group ^LG in terms of spherical perverse sheaves (or D-modules) on the affine Grassmannian Gr_G=G((t))/G[[t]] of the original group G. In the present paper we perform a first step in realizing the category of representations of the quantum group corresponding to ^LG in terms of the geometry of Gr_G. The idea of the construction belongs to Jacob Lurie.

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