Ulrich Thiel, Specialization theory.

Abstract:

I will give a general overview of specialization theory. In geometric terms, this theory is concerned with the understanding of representation-theoretic objects (e.g., blocks, simple modules, etc.) of the special fibers of a quasi-coherent sheaf of algebras on an irreducible affine scheme. The idea is to find ways to relate the objects of the special fibers to the corresponding objects of the generic fiber and to understand for which special fibers they remain the same. In down to earth terms, specialization theory provides a collection of techniques and results to systematically study algebras involving parameters like Hecke algebras and Cherednik algebras. The roots of this theory are classical results in modular representation theory of finite groups.