Wednesday, November 21, 2018 - 11:15
Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin, R. 2006
FS Algebra und Zahlentheorie
Prof. E. Große-Klönne
Hecke polynomials appear in the theory of Hecke operators on spaces of Siegel modular forms for the symplectic group. In order to study the relations between the Fourier coefficients and the eigenvalues of the eigenfunctions of the Hecke operators, it becomes necessary to decompose polynomials with coefficients in a spherical Hecke algebra inside a much larger parabolic Hecke algebra. Andrianov developed the tool of negative powers'' of Frobenius elements to give a simple criterion for such a decomposition. This method was subsequently used to prove a decomposition theorem for various other classical groups by Andrianov and Gritsenko. In this talk I will sketch a generalization of this method to the case of (connected) reductive groups over a local field satisfying a certain hypothesis. I will prove that this hypothesis is satisfied for reductive groups of semisimple rank 1.
submitted by Carmen Zyska (zyska@math.hu-berlin.de, +491627308953)