M.Sc Thesis
M.Sc Student Ozeri Dror Spherical Functions on 2-Adic Ramified Hermitian Spaces Department of Mathematics Professor Omer Offen Professor Ehud Moshe Baruch

Abstract

Let F/E be a quadratic extension of p-adic local fields. Y. Hironaka introduced the spherical functions on the p-adic space of Hermitian matrices: the common eigenfunctions of the associated Hecke algebra.  For the space of 2?2 Hermitian matrices, we complete Hironaka's work by also considering the case of a wildly ramified quadratic extension. We compute the spherical functions explicitly and obtain the functional equations. Our method involves brute force calculation of the spherical functions by direct integration. This integration turned out to be solvable by studying the interesting properties of the trace and the norm maps associated to the extension F/E.