On old and new Jacobi forms
\textit{M. Eichler} and \textit{D. Zagier} [The theory of Jacobi forms, Prog. Math. 55 (1985; Zbl 0554.10018)] introduced certain Hecke operators \(U_d\) and \(V_d\) on classical Jacobi forms. They change the index and are the basis for a theory of Jacobi old- and newforms. In the paper under review the author introduces certain index shifting operators for local and global representations of the Jacobi groups, which turn out to be compatible with the classical one. Moreover a purely local conjecture is formulated about the dimension of spaces of spherical vectors in representations of the \(p\)-adic Jacobi group. Evidence for this conjecture also comes from the ``certain space'' of modular forms by \textit{N. Skoruppa} and \textit{D. Zagier} [Invent. Math. 94, 113-146 (1988; Zbl 0651.10020)] and its local analogs.
scientific article; zbMATH DE number 1389289