The Weil Representations of the Jacobi Group
Jae-Hyun Yang
TL;DR
This paper investigates the Weil representations of the Jacobi group, exploring their properties and applications in automorphic forms and representation theory, thus advancing understanding in mathematical physics and number theory.
Contribution
It introduces a detailed study of Weil representations for the Jacobi group, highlighting their properties and applications in automorphic forms and representation theory.
Findings
Characterization of Weil representations of the Jacobi group
Applications to automorphic forms on the Jacobi group
Insights into the representation theory of the Jacobi group
Abstract
The Jacobi group is the semi-direct product of the symplectic group and the Heisenberg group. The Jacobi group is an important object in the framework of quantum mechanics, geometric quantization and 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 the Jacobi group and representation theory of the Jacobi group.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology