  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.
