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Theta series liftings from orthogonal groups to semi-simple groups

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  09 April 2009

Min Ho Lee
Min Ho Lee
Affiliation:
Department of Mathematics University of Northern lowaCedar Falls, IA 50614USA e-mail: lee@math. uni.edu
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Abstract

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We study a correspondence between automorphic forms on an orthogonal group and automorpbic forms on a semi-simple Lie group associated to an equivariant holomorphic map of a symmetric domain into a Siegel upper half space. We construct an automorphic form on the symmetric domain thatg corresponds to an automorphic form on an orthogonal group using theta series, and prove that such a correspondence is compatible with the appropriate Hecks operator actions on the corresponding automorphic forms. As an example, we describe the case of spin groups.

MSC classification

Secondary: 11F55: Other groups and their modular and automorphic forms (several variables) 11F27: Theta series; Weil representation; theta correspondences
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 1 , August 2000 , pp. 127 - 142
Copyright
Copyright © Australian Mathematical Society 2000

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