Faculty Publications
Poisson Liftings Of Holomorphic Automorphic Forms On Semisimple Lie Groups
Document Type
Article
Journal/Book/Conference Title
Journal of Lie Theory
Volume
10
Issue
1
First Page
81
Last Page
91
Abstract
Let G be a semisimple Lie group of Hermitian type, K ⊂ G a maximal compact subgroup, and P ⊂ G a minimal parabolic subgroup associated to K. If σ is a finite-dimensional representation of K in a complex vector space, it determines the associated homogeneous vector bundles on the homogeneous manifolds G/P and G/K. The Poisson transform associates to each section of the bundle over G/P a section of the bundle over G/K, and it generalizes the classical Poisson integral. Given a discrete subgroup Γ of G, we prove that the image of a Γ-invariant section of the bundle over G/P under the Poisson transform is a holomorphic automorphic form on G/K for Γ. We also discuss the special case of symplectic groups in connection with holomorphic forms on families of abelian varieties.
Department
Department of Mathematics
Original Publication Date
12-1-2000
Recommended Citation
Lee, Min Ho and Myung, Hyo Chul, "Poisson Liftings Of Holomorphic Automorphic Forms On Semisimple Lie Groups" (2000). Faculty Publications. 3605.
https://scholarworks.uni.edu/facpub/3605
