Tuesday, November 18, 14:00, 7.527
Ulrich Thiel, Specialization theory.
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.