On Jacobi forms of half-integral weight and matrix level

Abstract

TextIn this paper we will consider the Kohnen plus space for Hilbert-Siegel-Jacobi forms of half-integral weight and certain type of matrix index. As in the case of classical modular forms, the Jacobi forms in the Kohnen plus space are characterized by some restrictions on their Fourier coefficients. We will show that a Jacobi form of half-integral weight is in the Kohnen plus space if and only if the representation, which is generated by the form, of the adelic metaplectic double covering of the Jacobi group is equivalent to the Weil representation and use this equivalence condition to give an isomorphism of the Kohnen plus space with the space of Jacobi forms of certain corresponding integral weight and matrix index. Finally, we will see that the given isomorphism is a Hecke isomorphism with respect to the odd places of the underlying totally real number field. VideoFor a video summary of this paper, please visit https://youtu.be/J88ahOlr0GI.