Quantizing nilpotent coadjoint orbits
by
David A. Vogan
MIT, Cambridge, USA

The Kirillov-Kostant philosophy seeks to attach irreducible unitary representations of a Lie group G to the orbits of G on the dual of its Lie algebra. In order to implement this philosophy for all nice Lie groups (for example algebraic Lie groups), it remains only to attach unitary representations to nilpotent coadjoint orbits for real reductive Lie groups. There is a rather detailed prescription for how the construction of a unitary representation ought to proceed in this case, due in a key point to Ranee Brylinski. I'll describe this prescription as explicitly as possible, explaining what gaps remain to be filled.

Date received: April 17, 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-20.