## Y. Benoist, Y. Inoue, and T. Kobayashi.
Temperedness criterion of the tensor product of parabolic induction
for $GL_n$.
, Journal of Algebra
**617** (2023), 1-16,
DOI:
10.1016/j.jalgebra.2022.10.029.
arXiv: 2108.12125..

We give a necessary and sufficient condition for a pair of parabolic subgroups $P$ and $Q$ of $G=GL_n(\mathbb{R})$ 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 $G$.

[ DOI |
arXiv |
preprint version(pdf) ]

© Toshiyuki Kobayashi