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Theta functions and Weil representations of loop symplectic groups. (English) Zbl 1216.11051
Summary: We introduce Weil representations for loop symplectic groups and prove the convergence and modularity of the related theta functions.

MSC:
11F27 Theta series; Weil representation; theta correspondences
11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F85 \(p\)-adic theory, local fields
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