The Schroedinger-Weil Representation and Jacobi Forms of Half-Integral Weight

Abstract

In this paper, we define the concept of Jacobi forms of half-integral weight using Takase's automorohic factor of weight 1/2 for a two-fold covering group of the symplectic group on the Siegel upper half plane and find covariant maps for the Schroedinger-Weil representation. Using these covariant maps, we construct Jacobi forms of half-integral weight with respect to an arithmetic subgroup of the Jacobi group.

25 pages ; correction of many typos ; change of some notations

References in corpus (3)

• Invariant metrics and Laplacians on Siegel-Jacobi space
• Invariant metrics and Laplacians on Siegel-Jacobi Disk
• A note on a fundamental domain for Siegel-Jacobi space

Cited by in corpus (2)

• Gaussian distributions, Jacobi group and Siegel-Jacobi space
• The Weil Representations of the Jacobi Group