Semi-infinite cohomology and Kazhdan-Lusztig equivalence at positive level

Abstract

A positive level Kazhdan-Lusztig functor is defined using Arkhipov-Gaitsgory duality for affine Lie algebras. The functor sends objects in the DG category of G(O)-equivariant positive level affine Lie algebra modules to objects in the DG category of modules over Lusztig's quantum group at a root of unity. We prove that the semi-infinite cohomology functor for positive level modules factors through the Kazhdan-Lusztig functor at positive level and the quantum group cohomology functor with respect to the positive part of Lusztig's quantum group.

38 pages

References in corpus (3)

• Higher Topos Theory
• Compact generation of the category of D-modules on the stack of G-bundles on a curve
• The semi-infinite intersection cohomology sheaf

Cited by in corpus (1)

• Semi-infinite cohomology and the linkage principle for $W$-algebras