798 citations · 3.1k across the 77 of their papers we have counts for
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Is there an analytic theory of automorphic functions for complex algebraic curves?
Edward Frenkel
The geometric Langlands correspondence for complex algebraic curves differs from the original Langlands correspondence for number fields in that it is formulated in terms of sheave…
Langlands Program, Trace Formulas, and their Geometrization
Edward Frenkel
The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connec…
Geometrization of Trace Formulas
Edward Frenkel, Ngo Bao Chau
Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function…
Gauge Theory and Langlands Duality
Edward Frenkel
The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed wh…
Gerbal Representations of Double Loop Groups
Edward Frenkel, Xinwen Zhu
A crucial role in representation theory of loop groups of reductive Lie groups and their Lie algebras is played by their non-trivial second cohomology classes which give rise to th…
Any flat bundle on a punctured disc has an oper structure
Edward Frenkel, Xinwen Zhu
We prove that any flat G-bundle, where G is a complex connected reductive algebraic group, on the punctured disc admits the structure of an oper. This result is important in the lo…
D-modules on the affine flag variety and representations of affine Kac-Moody algebras
Edward Frenkel, Dennis Gaitsgory
We study the connection between the category of modules over the affine Kac-Moody Lie algebra at the critical level, and the category of D-modules on the affine flag scheme G((t))/…
Geometric realizations of Wakimoto modules at the critical level
E. Frenkel, D. Gaitsgory
We study the Wakimoto modules over the affine Kac-Moody algebras at the critical level from the point of view of the equivalences of categories proposed in our previous works, rela…
Localization of g^-modules on the affine Grassmannian
Edward Frenkel, Dennis Gaitsgory
We consider the category of modules over the affine Kac-Moody algebra g^ of critical level with regular central character. In our previous paper math.RT/0508382 we conjectured that…
Fusion and convolution: applications to affine Kac-Moody algebras at the critical level
Edward Frenkel, Dennis Gaitsgory
Let g be a semi-simple Lie algebra, and let g^ be the corresponding affine Kac-Moody algebra. Consider the category of g^-modules at the critical level, on which the action of the…
Local geometric Langlands correspondence and affine Kac-Moody algebras
Edward Frenkel, Dennis Gaitsgory
By a local geometric Langlands correspondence for a complex reductive group G we understand a construction which assigns to a local system on the punctured disc for the Langlands d…