Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590219 | Journal of Functional Analysis | 2014 | 35 Pages |
Abstract
Let G be a simple real Lie group with maximal parabolic subgroup P whose nilradical is abelian. Then X=G/PX=G/P is called a symmetric R-space. We study the degenerate principal series representations of G on C∞(X)C∞(X) in the case where P is not conjugate to its opposite parabolic. We find the points of reducibility, the composition series and all unitarizable constituents. Among the unitarizable constituents we identify some small representations having as associated variety the minimal nilpotent KCKC-orbit in pC⁎, where KCKC is the complexification of a maximal compact subgroup K⊆GK⊆G and g=k+pg=k+p the corresponding Cartan decomposition.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jan Möllers, Benjamin Schwarz,