A chiral Borel-Weil-Bott theorem
Algebraic Geometry
2011-12-13 v3 High Energy Physics - Theory
Representation Theory
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 -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.
Cite
@article{arxiv.0903.1281,
title = {A chiral Borel-Weil-Bott theorem},
author = {T. Arakawa and F. Malikov},
journal= {arXiv preprint arXiv:0903.1281},
year = {2011}
}
Comments
Some considerable reworking. A final version to appear in Adv. in Math