Localization of $\frak{u}$modules. IV. Localization on $\Bbb{P}^1$
Abstract
This article is a sequel to hepth/9411050, qalg/9412017, qalg/9503013. Given a collection of $m$ finite factorizable sheaves $\{\CX_k\}$, we construct here some perverse sheaves over configuration spaces of points on a projective line $\BP^1$ with $m$ additional marked points. We announce here (with sketch proof) the computation of the cohomology spaces of these sheaves. They turn out to coincide with certain "semiinfinite" $\Tor$ spaces of the corresponding $\fu$modules. As a corollary, we get a description of local systems of conformal blocks in WZW models in genus $0$ (cf. ~\cite{ms}) as natural subquotients of some semisimple local systems of geometric origin. In particular, these local systems are semisimple themselves.
 Publication:

eprint arXiv:qalg/950601
 Pub Date:
 June 1995
 arXiv:
 arXiv:qalg/9506011
 Bibcode:
 1995q.alg.....6011F
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 29 pages, amslatex. A minor correction is made