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A spectral gap property for subgroups of finite covolume in Lie groups

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Bekka B., Cornulier Y.

Colloquium Mathematicum

2010

tom 118

nr 1

175-182

Let G be a real Lie group and H a lattice or, more generally, a closed subgroup of finite covolume in G. We show that the unitary representation $λ_{G/H}$ of G on L²(G/H) has a spectral gap, that is, the restriction of $λ_{G/H}$ to the orthogonal complement of the constants in L²(G/H) does not have almost invariant vectors. This answers a question of G. Margulis. We give an application to the spectral geometry of locally symmetric Riemannian spaces of infinite volume.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Bekka B.

1 Cornulier Y.

1 2010

Wyniki wyszukiwania

A spectral gap property for subgroups of finite covolume in Lie groups