Geodesic
Tempered Homogeneous Spaces III
Journal of Lie theory, Tome 31 (2021) no. 3, pp. 833-869
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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.
Classification : 22E46, 43A85, 22F30
Mots-clés : Lie groups, homogeneous spaces, tempered representations, unitary representations, matrix coefficients, symmetric spaces 
@article{JLT_2021_31_3_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2021_31_3_JLT_2021_31_3_a9/}
}
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Y. Benoist; T. Kobayashi. Tempered Homogeneous Spaces III. Journal of Lie theory, Tome 31 (2021) no. 3, pp. 833-869. http://geodesic.mathdoc.fr/item/JLT_2021_31_3_JLT_2021_31_3_a9/