Localization of $\frak{u}$-modules. I. Intersection cohomology of real arrangements
Abstract
Description
This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a root of unity.
In the present paper we study perverse sheaves over a complex affine space which are smooth along the stratification determined by a finite arrangement of complex affine hyperplanes defined by real equations. In particular, we construct explicitely (in terms of combinatorial data) complexes computing cohomology of Goresky-MacPherson extensions of one-dimensional local systems over the complement of hyperplanes.
26 pages, amslatex. A misprint corrected
26 pages, amslatex. A misprint corrected