## Y. Benoist and T. Kobayashi, *Tempered homogeneous spaces III*, Journal
of Lie Theory **31** (2021), 833-869..

Let $G$ be a real semisimple algebraic Lie group and $H$ a real
reductive algebraic subgroup.
We describe the pairs $(G,H)$ for which the representation of $G$
in $L^2(G/H)$ is tempered.
When $G$ and $H$ are complex Lie groups,
the temperedness condition is characterized by the fact that
{\it the stabilizer in $H$ of a generic point on $G/H$ is virtually abelian}.

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© Toshiyuki Kobayashi