Title
Restrictions of certain degenerate principal series of the universal covering of the symplectic group
Document Type
Article
Publication Date
11-19-2010
Abstract
Let S̃p(n,ℝ) be the universal covering of the symplectic group. In this paper, we study the restrictions of the degenerate unitary principal series I(ε, t) of fSp(n,ℝ) onto S̃p(p,ℝ) S̃p(n - p,ℝ). We prove that if n ≥ 2p, I(ε, t)| S̃p(p,ℝ)fSp(n-p,ℝ) is unitarily equivalent to an L2 -space of sections of a homogeneous line bundle L 2(S̃p(n - p,ℝ) ̃ GL(n-2p)N ℂε,t+p) (see Theorem 1.1). We further study the restriction of complementary series C(ε, t) onto Ũ(n - p)S̃p(p,ℝ). We prove that this restriction is unitarily equivalent to I(ε, t)|Ũ (n-p)S̃p(p,ℝ) for t ̃ ε ℝ. Our results suggest that the direct integral decomposition of C(ε, t)| S̃p(p,ℝ)S̃p(n-p,ℝ) will produce certain complementary series for S̃p(n - p,ℝ) ([He09]). © 2010 Heldermann Verlag.
Publication Source (Journal or Book title)
Journal of Lie Theory
First Page
31
Last Page
48
Recommended Citation
He, H. (2010). Restrictions of certain degenerate principal series of the universal covering of the symplectic group. Journal of Lie Theory, 20 (1), 31-48. Retrieved from https://repository.lsu.edu/mathematics_pubs/476