Spherical representations of the Jacobi group
Let \(G^J\) be the Jacobi group over a \(p\)-adic field. The author continues the earlier work (with \textit{R. Berndt}) [Elements of the representation theory of the Jacobi group. Progress in Mathematics 163, Birkhäuser, Basel (1998; Zbl 0931.11013)] and determines spherical vectors for admissible \(G^J\)-representations by explicit calculations in certain models. This leads to a complete classification of spherical representations in the ``almost good'' case: Besides the expected spherical principal series representations there are exactly three more. These can be explicitly associated to characters of the Hecke algebra. This result explains the local factors attached to a cuspidal Jacobi eigenform of squarefree index by \textit{J. Dulinski} [Result. Math. 31, 75-94 (1997; Zbl 0880.11044)].
scientific article; zbMATH DE number 1416672
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