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tempered unitary representations

Journal of the Institute of Mathematics of Jussieu (1)

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TEMPERED HOMOGENEOUS SPACES IV
Part of
- Abstract harmonic analysis
- Noncompact transformation groups
Yves Benoist, Toshiyuki Kobayashi
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 6 / November 2023

Published online by Cambridge University Press:

07 June 2022, pp. 2879-2906

Print publication:

November 2023
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Let G be a complex semisimple Lie group and H a complex closed connected subgroup. Let and 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 in contains regular elements by showing simultaneously the equivalence to other striking conditions, such as has a solvable limit algebra.