A chiral Borel-Weil-Bott theorem

Abstract

We compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold. This is applied to (1) finding the character of $G$-integrable irreducible highest weight modules over the affine Lie algebra at the critical level, and (2) computing a certain elliptic genus of the flag manifold. The main tool is a result that interprets the Drinfeld-Sokolov reduction as a derived functor.

Some considerable reworking. A final version to appear in Adv. in Math

References in corpus (7)

• Vertex Algebras and Algebraic Curves
• Elliptic Genera and Applications to Mirror Symmetry
• Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction
• Weyl modules and opers without monodromy
• Local Geometric Langlands Correspondence: the Spherical Case
• Characters of representations of affine Kac-Moody Lie algebras at the critical level
• Algebras of twisted chiral differential operators and affine localization of $\mathfrak{g}$-modules

Cited by in corpus (1)

• Quasi-Topological Gauged Sigma Models, The Geometric Langlands Program, And Knots