Periods of Saito–Kurokawa Representations

Abstract

Suppose that Π is an irreducible unitary automorphic representation in the discreet spectrum of and Π′ an irreducible cuspidal unitary representation of ⁠. When Π is in the Saito–Kurokawa packet, we show that the square of the global SO4-period of Π⊗Π′, when nonvanishing, is a product of local periods defined by regularized integrals of matrix coefficients.