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

TL;DR

This paper introduces a new framework for Jacobi forms of half-integral weight using the Schroedinger-Weil representation, expanding the understanding of automorphic forms on covering groups.

Contribution

It defines Jacobi forms of half-integral weight via Takase's automorphic factor and constructs them using covariant maps related to the Schroedinger-Weil representation.

Findings

Defined Jacobi forms of half-integral weight using automorphic factors

Constructed Jacobi forms with respect to arithmetic subgroups

Connected covariant maps to the Schroedinger-Weil representation

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.