The Weil representations of the Jacobi group

초록

A Jacobi group plays an important role in arithmetic, geometry and representation theory. A Jacobi group is an important object in the framework of quantum mechanics, geomeric quantization and quantum optics. In this paper we study the Weil representations of the Jacobi group and their properties. We also provide their applications to the theory of automorphic forms on a Jacobi group and representation theory of a Jacobi group.