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
Recommended Citation
Hongyu, H. (2011). Unitary representations and the heisenberg parabolic subgroup. Journal of Lie Theory, 21 (4), 847-860. Retrieved from https://repository.lsu.edu/mathematics_pubs/1500