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Theta functions on Hermitian symmetric domains and fock representations

Part of: Lie groups Discontinuous groups and automorphic forms Abelian varieties and schemes

Published online by Cambridge University Press:  09 April 2009

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

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One way of realizing representations of the Heisenberg group is by using Fock representations, whose representation spaces are Hilbert spaces of functions on complex vector space with inner products associated to points on a Siegel upper half space. We generalize such Fock representations using inner products associated to points on a Hermitian symmetric domain that is mapped into a Seigel upper half space by an equivariant holomorphic map. The representations of the Heisenberg group are then given by an automorphy factor associated to a Kuga fiber variety. We introduce theta functions associated to an equivariant holomorphic map and study connections between such generalized theta functions and Fock representations described above. Furthermore, we discuss Jacobi forms on Hermitian symmetric domains in connection with twisted torus bundles over symmetric spaces.

MSC classification

Secondary: 22E45: Representations of Lie and linear algebraic groups over real fields 11F55: Other groups and their modular and automorphic forms (several variables) 11F27: Theta series; Weil representation; theta correspondences 14K10: Algebraic moduli, classification 14K25: Theta functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 201 - 234
Copyright
Copyright © Australian Mathematical Society 2003

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