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

Bachir Bekka, and Yves Cornulier. "A spectral gap property for subgroups of finite covolume in Lie groups." Colloquium Mathematicae 118.1 (2010): 175-182. <http://eudml.org/doc/283825>.

@article{BachirBekka2010,
abstract = {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.},
author = {Bachir Bekka, Yves Cornulier},
journal = {Colloquium Mathematicae},
keywords = {lattice; spectral gap; Lie group; spectral geometry},
language = {eng},
number = {1},
pages = {175-182},
title = {A spectral gap property for subgroups of finite covolume in Lie groups},
url = {http://eudml.org/doc/283825},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Bachir Bekka
AU - Yves Cornulier
TI - A spectral gap property for subgroups of finite covolume in Lie groups
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 1
SP - 175
EP - 182
AB - 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.
LA - eng
KW - lattice; spectral gap; Lie group; spectral geometry
UR - http://eudml.org/doc/283825
ER -