J. Aust. Math. Soc.
74 (2003), 201-234
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Theta functions on Hermitian symmetric domains and Fock representations
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Min Ho Lee
Department of Mathematics
University of Northern Iowa
Cedar Falls, Iowa 50614
USA
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 Siegel 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.
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