Nilpotents orbits for Sp(p,q) and U(p,q) and classification problems.

In this talk, I’ll review the theory of blocks and cells of Harish-Chandra modules of regular integral infinitesimal character and discuss the role nilpotent orbits play in their classification. I’ll describe the combinatorics of those orbits for the group Sp(p,q), and explain how this allows us to give a classification of associated varieties of certain generalized Harish-Chandra modules, as part of a program of Penkov and Zuckerman. If time permits, I’ll end with a similar classification for U(p,q) and discuss the differences between the two cases.