Invariant measures on homogeneous spaces, with applications to function spaces and lattice counting

Bernhard Krötz; Eitan Sayag; Henrik Schlichtkrull

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arXiv · 1004.1942

Invariant measures on homogeneous spaces, with applications to function spaces and lattice counting

Bernhard Krötz·Eitan Sayag·Henrik Schlichtkrull

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Abstract

Let G be a real reductive group and G/H a unimodular homogeneous G space with a closed connected subgroup H. We establish estimates for the invariant measure on G/H. Using these, we prove that all smooth vectors in the Banach representation L^p(G/H) of G are functions that vanish at infinity if and only if G/H is of reductive type. An application to lattice counting on G/H is presented.

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BibTeX RIS

Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull. 2011-06-20. Invariant measures on homogeneous spaces, with applications to function spaces and lattice counting. https://arxiv.org/abs/1004.1942

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