In 2015, Hayashida showed that, in consideration of the underlying field $\mathbb{Q}$, Kohnen plus space for Jacobi forms of half-integral weight $k + 1/2$ and certain matrix index is Hecke isomorphic to a space of Jacobi forms of weight $k + 1$ and certain matrix index. In this talk, we extend his result to the case for arbitrary totally real number fields. We will give a representation theoretical equivalent condition for a Jacobi form to be in the plus space, from which the isomorphism above follows immediately. Also, we will illustrate why the isomorphism is a Hecke isomorphism with respect to odd places of the underlying totally real number field. This is fairly easy to see through the consideration of Schroedinger-Weil representation.

本セミナーは Zoom を使ってオンラインで開催しました．

The seminar was organized by Zoom.