Discretely decomposable unitary representations and a proof of Kobayashi's conjectures
by
Jing-Song Huang
Dept. of Math., Hong Kong Univ. of Sci. and Tech., Hong Kong

Let G be a reductive Lie group and K the maximal compact subgroup of G corresponding to a Cartan involution \theta. Let G' be a \theta-stable symmetric subgroup with the maximal compact subgroup K'=3DK \cap G'. Assume that \pi is an irreducible unitary representation of G. The aim of this talk is to present a joint work with David Vogan showing that the restriction \pi|_K' is K'-admissible if and only if the associate variety of (the Harish-Chandra module of) \pi has an open K'_\noexpand -orbit. In particular, this gives a criterion for the restriction \pi|_G' to be decomposed discretely on G'. As a consequence, we prove three conjectures of Kobayashi [K].

[K] T. Kobayashi, Discrete decomposable restrictions of unitary representations of reductive Lie groups - examples and conjectures, Advanced Studies in Pure Mathematics 26, 2000, 99-127

Date received: May 16, 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-46.