A spectral gap property for subgroups of finite covolume in Lie groups
Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 175-182
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
real lie group lattice generally closed subgroup finite covolume unitary representation lambda has spectral gap restriction lambda orthogonal complement constants does have almost invariant vectors answers question margulis application spectral geometry locally symmetric riemannian spaces infinite volume
Affiliations des auteurs :
Bachir Bekka 1 ; Yves Cornulier 2
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author = {Bachir Bekka and Yves Cornulier},
title = {A spectral gap property for subgroups of finite covolume in {Lie} groups},
journal = {Colloquium Mathematicum},
pages = {175--182},
publisher = {mathdoc},
volume = {118},
number = {1},
year = {2010},
doi = {10.4064/cm118-1-9},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm118-1-9/}
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Bachir Bekka; Yves Cornulier. A spectral gap property for subgroups of finite covolume in Lie groups. Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 175-182. doi: 10.4064/cm118-1-9
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