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

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

2010-04-12

arxiv.org/abs/1004.1942v2

Mathematics

Representation Theory

An expanded version entitled "Decay on homogeneous spaces of reductive type" was posted as article 1106.1331

Scientific paper

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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