Relative Discrete Series Representations for Two Quotients ofp-adic GLn

Abstract

AbstractWe provide an explicit construction of representations in the discrete spectrum of twop-adic symmetric spaces. We consider GLn(F) × GLn(F)\GL2n(F) and GLn(F)\GLn(E), whereEis a quadratic Galois extension of a nonarchimedean local fieldFof characteristic zero and odd residual characteristic. The proof of the main result involves an application of a symmetric space version of Casselman’s Criterion for square integrability due to Kato and Takano.