Fourier-Sato transform and Lusztig symmetries

In this talk I will explain how to compute,  in terms of linear algebra data, the Fourier-Sato
transform of perverse sheaves over a complex affine space, smooth along a hyperplane arrangement.
As an example a geometric interpretation, and a generalization, of Lusztig's braid group action on
representations of quantum groups will be given. A joint work with M. Finkelberg and M. Kapranov