REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: Let G be an algebraic supergroup over C with reductive underlying even group. The category of representations of G is not semisimple and has rather complicated structure. In this talk we concentrate on studying restriction and induction functors for different subgroups K of G and, in particular, on the question when the restriction map Ext_G(X,Y) to Ext_K(X,Y) between Ext groups is injective for all G-modules X and Y. This question is closely related to understanding the ring of regular functions on G/K as a G-module. We report on some results in the case when G/K is a symmetric superspace and answer the main question for some supergroups G. We also discuss the connection with work of Boe, Kujawa and Nakano on support varieties for supergroups. This is a joint project with Alex Sherman.