Colloquium: Tuesday, May 31, 2 pm. Speaker: Dmitry Gourevitch (Weizmann). Title: “D-modules and equivariant distributions – old and new”.
I will first recall the notions of Schwartz functions and tempered distributions – on the line and then on general real affine algebraic manifolds.
Then I will pose a problem on the existence of distributions that are semi-invariant under a group action.
Next I will recall some notions in the theory of D-modules, i.e. modules over the algebra of polynomial differential operators, and indicate a classical solution to this problem, due to Bernstein and Saito.
Then I will present a generalization of this solution, due to Sahi, Sayag and myself.
Finally, I will explain the relation of this problem to relative representation theory or real reductive groups.
If time permits, we will discuss also how to bound the dimension of the space of semi-invariant distributions using D-modules.
