Journal of Lie Theory

no. 3
Tempered Homogeneous Spaces III
Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 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 L2(G/H) is tempered. The proof gives the complete list of pairs (G,H) for which L2(G/H) is not tempered. When G and H are complex Lie groups, the temperedness condition is characterized by the fact that the stabilizer in H of a generic point on G/H is virtually abelian.
DOI: 10.5802/jolt.1197
Classification: 22E46, 43A85, 22F30
Keywords: Lie groups, homogeneous spaces, tempered representations, unitary representations, matrix coefficients, symmetric spaces 
@article{JOLT_2021_31_3_a9,
     author = {Y. Benoist and T. Kobayashi},
     title = {Tempered {Homogeneous} {Spaces} {III}},
     journal = {Journal of Lie Theory},
     pages = {833--869},
     year = {2021},
     volume = {31},
     number = {3},
     doi = {10.5802/jolt.1197},
     zbl = {1483.22009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1197/}
}
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Y. Benoist; T. Kobayashi. Tempered Homogeneous Spaces III. Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 833-869. doi: 10.5802/jolt.1197

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