798 citations · 3.1k across the 77 of their papers we have counts for
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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))/…
Local Geometric Langlands Correspondence: the Spherical Case
Edward Frenkel, Dennis Gaitsgory
A module over an affine Kac--Moody algebra g^ is called spherical if the action of the Lie subalgebra g[[t]] on it integrates to an algebraic action of the corresponding group G[[t…
Geometric Endoscopy and Mirror Symmetry
Edward Frenkel, Edward Witten
The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups. This mirror symmetry, in turn, reduces t…
Weyl modules and opers without monodromy
Edward Frenkel, Dennis Gaitsgory
We prove that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with regula…
Quantization of soliton systems and Langlands duality
Boris Feigin, Edward Frenkel
We consider the problem of quantization of classical soliton integrable systems, such as the KdV hierarchy, in the framework of a general formalism of Gaudin models associated to a…
Notes on instantons in topological field theory and beyond
E. Frenkel, A. Losev, N. Nekrasov
This is a brief summary of our studies of quantum field theories in a special limit in which the instantons are present, the anti-instantons are absent, and the perturbative correc…