Jacobi Forms of Degree One and Weil Representations

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We discuss the notion of Jacobi forms of degree one with matrix index, we state dimension formulas, give explicit examples, and indicate how closely their theory is connected to the theory of invariants of Weil representations associated to finite quadratic modules.
Contribution for the Proceedings of the Conference Siegel Modular Forms and Abelian Varieties at Lake Hamana 2007

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