The Weil Representations of the Jacobi Group

2009/07/26 by Jae-Hyun Yang, Yang, Jae-Hyun
Mathematics · #11F27 #11F37 #11F50 #53D12 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F27 #msc:11F37 #msc:11F50 #msc:53D12

paper · pdf · doi:10.48550/arxiv.0907.4526

30 pages : Correction of typos ; added reference

openalex publication_date 2009/07/26 · arxiv created 2009/08/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Heegner points, cycles and Maass forms
• The Schroedinger-Weil Representation and Jacobi Forms of Half-Integral Weight
• On Modular Forms of Half Integral Weight

Related

• Theta Series Associated with the Weil-Schroedinger Representation
• The Schroedinger-Weil Representation and Jacobi Forms of Half-Integral Weight
• On the lattice model of the Weil representation
• Jacobi Forms of Degree One and Weil Representations
• Applications of the Jacobi group to Quantum Mechanics