Temperedness of reductive homogeneous spaces

Abstract

Let G be a semisimple algebraic Lie group and H a reductive subgroup. We find geometrically the best even integer p for which the representation of G in L^2(G/H) is almost L^{p}. As an application, we give a criterion which detects whether this representation is tempered.

to appear in Journal of European Mathematical Society

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• Topics on global analysis of manifolds and representation theory of reductive groups
• Recent advances in branching problems of representations
• Temperedness criterion of the tensor product of parabolic induction for $G{L}_n$
• A note on $L^p$-factorizations of representations