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

• Autorzy: Bachir Bekka , Yves Cornulier
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A30: Ergodic theorems, spectral theory, Markov operators
• 43A85: Analysis on homogeneous spaces
• 22E40: Discrete subgroups of Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 1
• Strony: 175-182

Daty

wydano

2010

Twórcy

autor

Bachir Bekka

• IRMAR, UMR 6625 du CNRS, Université de Rennes 1, Campus Beaulieu, F-35042 Rennes Cedex, France

autor

Yves Cornulier

• IRMAR, UMR 6625 du CNRS, Université de Rennes 1, Campus Beaulieu, F-35042 Rennes Cedex, France

Identyfikatory

DOI

10.4064/cm118-1-9