Twisted Whittaker model and factorizable sheaves

By D. Gaitsgory. 2007

67 citations recorded by the source corpus.

Abstract.Let G be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group Ğ in terms of spherical perverse sheaves (or D-modules) on the affine Grassmannian GrG = 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 Ğ in terms of the geometry of GrG. The idea of the construction belongs to Jacob Lurie.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e00cb0ea57a7bc84000e10b160c8c3818f8b198

How researchers see this paper

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In Algebra and Number Theory

1. E. Witten
2. A. Okounkov
3. J. Teschner
4. David Ben-Zvi
5. Joel Kamnitzer
6. Greg Kuperberg
7. D. Nadler
8. Bruce Fontaine

In Geometry and Topology

1. E. Witten
2. David Ben-Zvi
3. D. Nadler
4. A. Okounkov
5. J. Teschner
6. D. Gaiotto
7. Joel Kamnitzer
8. Greg Kuperberg

In Mathematical Physics

1. E. Witten
2. D. Nadler
3. David Ben-Zvi
4. A. Okounkov
5. J. Teschner
6. D. Gaiotto
7. Sergei Gukov
8. Joel Kamnitzer

Citations in the corpus

• Betti Geometric Langlands (2016, background): “he Kazhdan-Lusztig category of bg at level k∨ to Dk∨ (BunG∨(X)) discussed in Section 3.13.1 with a Poincar´e series functor from twisted Whittaker sheaves on the Grassmannian at x to Dk(BunG(X)), see [G2]. The Betti category ShvN(BunG(X)) also admits a natural twisted version, given by monodromic sh”
• Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I (2010, background): “to defining “quantum” versions of the geometric Langlands correspondence have been discussed in [24,26,40,67].”
• Lectures on K-theoretic computations in enumerative geometry (2015, background): “It is a very important property, much discussed in the literature, with slightly different definitions in different contexts, see for example [9, 34].”
• Buildings, spiders, and geometric Satake (2011, methodology): “Hopefully, we can extend to general q using the quantum geometric Satake developed by Gaitsgory (see [Gai08]).”
• Fivebranes and Knots (2011, background): “This generalization has been related to the theory of quantum groups [64], suggesting that geometric Langlands should be related to Chern-Simons theory.”