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

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