Temperedness criterion of the tensor product of parabolic induction for GLn

Abstract

We give a necessary and sufficient condition for a pair of parabolic subgroups P and Q of G=GLn(R) such that the tensor product of any two unitarily induced representations from P and Q are tempered. We also give an Lp-estimate of matrix coefficients of the regular representations on L2(G/L) when L is a Levi subgroup of G.