Unitary representations and the heisenberg parabolic subgroup

Document Type

Article

Publication Date

7-11-2011

Abstract

In this paper, we study the restriction of an irreducible unitary representation π of the universal covering S̃p2n(ℝ) to a Heisenberg maximal parabolic subgroup P̃. We prove that if π|P̃ is irreducible, then π must be a highest weight module or a lowest weight module. This is in sharp contrast with the GLn(ℝ) case. In addition, we show that for a unitary highest or lowest weight module, π|P̃ decomposes discretely. We also treat the groups U(p,q) and O*(2n). © 2011 Heldermann Verlag.

Publication Source (Journal or Book title)

Journal of Lie Theory

First Page

847

Last Page

860

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