Mathematics

By now, there is a fairly complete theory of the "flag varieties" of the classical  complex ind-groups GL(infty), O(infty), Sp(infty).These "flag varieties" are ind-varieties, and their points are certain infinite chains of subspaces which we refer to as generalized flags. In the course of this study some new facts about embeddings of flag varieties, in particular about embeddings of grassmannianshave been established. The purpose of this talk is to outline a future theory of ind-supervarieties of generalized flags, starting with a conjecture about certain embeddings of supergrassmannians.