## Duke Mathematical Journal

### D-modules on the affine Grassmannian and representations of affine Kac-Moody algebras

#### 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.

#### Article information

Source
Duke Math. J., Volume 125, Number 2 (2004), 279-327.

Dates
First available in Project Euclid: 27 October 2004

https://projecteuclid.org/euclid.dmj/1098892271

Digital Object Identifier
doi:10.1215/S0012-7094-04-12524-2

Mathematical Reviews number (MathSciNet)
MR2096675

Zentralblatt MATH identifier
1107.17013

Subjects
Primary: 17B67 81R10

#### Citation

Frenkel, Edward; Gaitsgory, Dennis. D-modules on the affine Grassmannian and representations of affine Kac-Moody algebras. Duke Math. J. 125 (2004), no. 2, 279--327. doi:10.1215/S0012-7094-04-12524-2. https://projecteuclid.org/euclid.dmj/1098892271

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