Localization of $\frak{u}$-modules. I. Intersection cohomology of real arrangements

Details Localization of $\frak{u}$-modules. I. Intersection cohomology of real arrangements Localization of $\frak{u}$-modules. I. Intersection cohomology of real arrangements

1994-11-07

arxiv.org/abs/hep-th/9411050v3

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, amslatex. A misprint corrected

Scientific paper

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.

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