Geodesic
A Description of Smooth Vectors of the Weil Representation in the Geometric Realization
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 90-93

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We describe the image of the Weil representation of the double covering of the symplectic group in the Schwartz space in the so-called geometric realization, i.e., in holomorphic functions on the symmetric domain called the Siegel upper half-plane.
Keywords: Weil representation, Schwartz space, Siegel upper half-plane. 
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     title = {A {Description} of {Smooth} {Vectors} of the {Weil} {Representation} in the {Geometric} {Realization}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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A. V. Stoyanovskii. A Description of Smooth Vectors of the Weil Representation in the Geometric Realization. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 90-93. http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a12/