On the characterization of skew-holomorphic Jacobi-forms
The author and \textit{S. Böcherer} [Math. Z. 204, 13-44 (1990; Zbl 0695.10024)] have given a characterization of the space of holomorphic Jacobi forms of weight \(k\) and index \(m\) in the sense of Eichler-Zagier in terms of the discrete series representation \(\pi^+_{m,k}\) of the Jacobi group. Meanwhile \textit{N. P. Skoruppa} [in Automorphic functions and their applications, Int. Conf., Khabarovsk/USSR 1988, 167-185 (1990; Zbl 0745.11029)] also introduced skew-holomorphic Jacobi forms. The author shows that they can be characterized as functions on the Jacobi group realizing vectors of dominant weight for the discrete series representation \(\pi^-_{m,k}\).
scientific article; zbMATH DE number 878388