## Y. Benoist and T. Kobayashi.
Tempered homogeneous spaces IV.
Journal of the Institute of Mathematics of Jussieu (2022), 1-28,
arXiv: 2009.10391.
DOI:
10.1017/S1474748022000287. Published on line, First View: 07 June, 2022.

Let $G$ be a complex semisimple Lie group
and $H$ a complex closed connected subgroup.
Let $\mathfrak{g}$ and $\mathfrak{h}$ be their Lie algebras.
We prove that the regular representation of $G$
in $L^2(G/H)$ is tempered if and only
if the orthogonal of $\mathfrak{h}$ in $\mathfrak{g}$
contains regular elements
by showing simultaneously the equivalence
to other striking conditions
such as $\mathfrak{h}$ has a solvable limit algebra.

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related papers: Part I, Part II, Part III ]

© Toshiyuki Kobayashi