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- W3034739204 abstract "We study the critical exponents of discrete subgroups of a higher rank semi-simple real linear Lie group $G$. Let us fix a Cartan subspace $mathfrak asubset mathfrak g$ of the Lie algebra of $G$. We show that if $Gamma< G$ is a discrete group, and $Gamma' triangleleft Gamma$ is a Zariski dense normal subgroup, then the limit cones of $Gamma$ and $Gamma'$ in $mathfrak a$ coincide. Moreover, for all linear form $phi : mathfrak ato mathbb R$ positive on this limit cone, the critical exponents in the direction of $phi$ satisfy $displaystyle delta_phi(Gamma') geq frac 1 2 delta_phi(Gamma)$. Eventually, we show that if $Gamma'backslash Gamma$ is amenable, these critical exponents coincide." @default.
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- W3034739204 date "2020-06-09" @default.
- W3034739204 modified "2023-09-26" @default.
- W3034739204 title "Critical exponents of normal subgroups in higher rank" @default.
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