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1 November 2004 D-modules on the affine Grassmannian and representations of affine Kac-Moody algebras
Edward Frenkel, Dennis Gaitsgory
Duke Math. J. 125(2): 279-327 (1 November 2004). DOI: 10.1215/S0012-7094-04-12524-2

Abstract

Let $\mathfrak{g}$ be a simple Lie algebra. For a level κ (thought of as a symmetric $\mathfrak{g}$-invariant form of $\mathfrak{g}$, let $\hat{\mathfrak{g}}_\kappa$ be the corresponding affine Kac-Moody algebra. Let GrG be the affine Grassmannian of $\mathfrak{g}$, and let Dκ(GrG)-mod be the category of κ-twisted right D-modules on GrG. By taking global sections of a D-module we obtain a functor Γ:Dκ(GrG)-mod → $\mathfrak{g}$κ-mod. It is known that this functor is exact and faithful when κ is less than critical or irrational. In this paper, we show that the functor Γ is also exact and faithful when κ is the critical level.

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Edward Frenkel. Dennis Gaitsgory. "D-modules on the affine Grassmannian and representations of affine Kac-Moody algebras." Duke Math. J. 125 (2) 279 - 327, 1 November 2004. https://doi.org/10.1215/S0012-7094-04-12524-2

Information

Published: 1 November 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1107.17013
MathSciNet: MR2096675
Digital Object Identifier: 10.1215/S0012-7094-04-12524-2

Subjects:
Primary: 17B67 81R10

Rights: Copyright © 2004 Duke University Press

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Vol.125 • No. 2 • 1 November 2004
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