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Now showing items 1-10 of 21

#### D-Modules on the Affine Flag Variety and Representations of Affine Kac-Moody Algebras

(American Mathematical Society, 2009)

The present paper studies 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 \(G((t))/I\), where \(I\) is the ...

#### Chiral Koszul Duality

(Springer, 2012)

We extend the theory of chiral and factorization algebras, developed for
curves by Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), ...

#### A Corollary of the B-function Lemma

(Birkhäuser Basel, 2011)

Let \(X\) be an algebraic variety, \(f\) a regular function, \(j:U \hookrightarrow X\) the complement to the locus of vanishing of \(f\), and \(M\) a holonomic D-module on \(U\). Consider the \(D_U[s]\)-module \(M\otimes ...

#### Twisted Whittaker Model and Factorizable Sheaves

(Birkhaeuser Verlag AG, 2008)

Let \(G\) be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group \(\check G\) in terms of spherical perverse sheaves (or D-modules) on the affine ...

#### Localization of \(\hat{\mathfrak{g}}\)-modules on the Affine Grassmannian

(Princeton University, 2009)

We consider the category of modules over the affine Kac-Moody algebra \(\hat{\mathfrak{g}}\) of critical level with regular central character. In our previous paper we conjectured that this category is equivalent to the ...

#### DG Indschemes

(American Mathematical Society, 2014)

We develop the notion of indscheme in the context of derived algebraic geometry, and study the categories of quasi-coherent sheaves and ind-coherent sheaves on indschemes. The main results concern the relation between ...

#### Deformations of Local Systems and Eisenstein Series

(Springer Science + Business Media, 2008)

#### Weyl Modules and Opers without Monodromy

(Springer-Verlag, 2010)

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 regular singularity and residue determined by ...

#### On Some Finiteness Questions for Algebraic Stacks

(Springer Science + Business Media, 2013)

We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of global sections on the DG ...

#### Hecke Operators on Quasimaps into Horospherical Varieties

(University Bielefeld, Fakultat Mathematik, 2009)

Let G be a connected reductive complex algebraic group. This paper and its companion [GN06] are devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought ...