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

Tom 118 / 2010

Bachir Bekka, Yves Cornulier Colloquium Mathematicum 118 (2010), 175-182 MSC: 22E40, 37A30, 43A85. DOI: 10.4064/cm118-1-9

Streszczenie

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 $\lambda _{G/H}$ of $G$ on $L^2(G/H)$ has a spectral gap, that is, the restriction of $\lambda _{G/H}$ to the orthogonal complement of the constants in $L^2(G/H)$ 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.

Autorzy

  • Bachir BekkaIRMAR, UMR 6625 du CNRS
    Université de Rennes 1
    Campus Beaulieu
    F-35042 Rennes Cedex, France
    e-mail
  • Yves CornulierIRMAR, UMR 6625 du CNRS,
    Université de Rennes 1
    Campus Beaulieu
    F-35042 Rennes Cedex, France
    e-mail

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