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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…
Lectures on the Langlands Program and Conformal Field Theory
Edward Frenkel
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introdu…
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…
Mirror symmetry in two steps: A-I-B
Edward Frenkel, Andrei Losev
We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric varie…