Spherical functions on U(n,n)/(U(n) × U(n)) and hermitian Siegel series

2009/04/28 by Hironaka, Yumiko
#11E95 #11F70 #11F85 #22E50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0904.4304

Abstract

We study spherical functions on the space isomorphic to U(2n)/(U(n)× U(n)) over a p-adic field; those functional equations with respect to the action of the Weyl group, the location of possible poles and zeros, explicit formulas, and spherical Fourier transforms. Then, as an application, we give a functional equation of p-adic local hermitian Siegel series.

Related

• Spherical functions on the space of p-adic unitary hermitian matrices
• Spherical functions on p-adic homogeneous spaces
• Spherical Functions on 2-adic Ramified Hermetian Spaces
• Spherical functions on symmetric spaces of Friedberg-Jacquet type
• Spherical functions on spherical varieties