On certain categories of modules and some related geometric notions
by
Boris Širola
Department of Mathematics, University of Zagreb, Croatia

Suppose Q is a connected closed subgroup of GL(n,F); F an algebraically closed field of characteristic zero. Let q be the Lie algebra of Q, and n an ideal of q. Denote by C the category of q-modules which are finitely generated as n-modules. In our talk we will explain why it would be interesting to find and understand a certain 'nice' subcategory of C, as was suggested by Casselman and Osborne. Related to that, we would like to understand the set of primes of U(n) which are Q-stable with respect to the adjoint representation. Furthermore, we will give some evidence that for n nilpotent, this set is closely related to the space of coadjoint Q-orbits on the dual of n; in particular, the closed orbit(s) correspond to the Q-stable primitive ideal(s). We will also introduce certain notions/ideas of 'geometric nature', and explain their relevance for studying the modules from the category C.

Date received: May 22, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagt-49.