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Brief communications

A Description of Smooth Vectors of the Weil Representation in the Geometric Realization

A. V. Stoyanovskii

Independent University of Moscow

Abstract: 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.

UDC: 512.815

Received: 08.02.2005

DOI: 10.4213/faa750

 English version: Functional Analysis and Its Applications, 2006, 40:3, 241–243

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