Abstract
The main result is an application of A. Weil's method of theta functions (Coll. Papers, vol. III, 1–69) and states that, for any locally compact commutative group G isomorphic to its dual, there is an injective representation of the symplectic group Sp(G) by a certain group of unitary operators in L 2( G × G) containing the Fourier transformation (in a slightly modified form).
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