Temperedness criterion of the tensor product of parabolic induction for $G{L}_n$

Abstract

We give a necessary and sufficient condition for a pair of parabolic subgroups $P$ and $Q$ of $G=G{L}_n(\mathbb{R})$ such that the tensor product of any two unitarily induced representations from $P$ and $Q$ are tempered. We also give an $L^p$-estimate of matrix coefficients of the regular representations on $L^2(G/L)$ when $L$ is a Levi subgroup of $G$.

Final version, to appear in Journal of Algebra

References in corpus (3)

• Finite multiplicity theorems for induction and restriction
• Temperedness of reductive homogeneous spaces
• Tempered homogeneous spaces III