Tempered homogeneous spaces III

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 the stabilizer in H of a generic point on G/H is virtually abelian.

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