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arXiv · 2205.11146

Inexistence de pavages mesurables invariants par un r\'eseau dans un espace homog\`ene d'un groupe de Lie simple

Félix Lequen
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Abstract

We prove that an homogeneous space of an almost simple Lie group does not have any measurable tiling invariant by a lattice of the Lie group. This refines the Howe-Moore ergodicity theorem. -- On d\'emontre qu'un espace homog\`ene d'un groupe de Lie presque simple n'admet pas de pavage mesurable invariant par un r\'eseau du groupe de Lie. Ceci constitue un raffinement du th\'eor\`eme d'ergodicit\'e de Howe-Moore.

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Félix Lequen. 2022-05-23. Inexistence de pavages mesurables invariants par un r\'eseau dans un espace homog\`ene d'un groupe de Lie simple. https://arxiv.org/abs/2205.11146

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