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Journal of Lie Theory, Vol. 11, No. 2, pp. 545-557 (2001)
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Jacobi Forms on Symmetric Domains and Torus Bundles over Abelian Schemes

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Min Ho Lee

Department of Mathematics

University of Northern Iowa

Cedar Falls, Iowa 50614

U. S. A.

lee@math.uni.edu

**Abstract:** We introduce Jacobi forms on Hermitian symmetric domains using automorphy factors associated to torus bundles over abelian schemes. We discuss families of modular forms determined by such Jacobi forms and prove that these Jacobi forms reduce to the usual Jacobi forms of several variables when the Hermitian symmetric domain is a Siegel upper half space.

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