Let $G$ be a semisimple algebraic Lie group and $H$ a reductive subgroup. We find geometrically the best even integer $p$ for which the representation of $G$ in $L^2(G/H)$ is almost $L^p$. As an application, we give a criterion which detects whether this representation is tempered.

We show that the automorphism group Aut([0,1],λ) of the Lebesgue measure has no non-trivial subgroups of index $<2^{\omega }$.

En théorie des groupes, le théorème de Kurosh est un résultat de structure concernant les sous-groupes d’un produit libre de groupes. Le théorème principal de cet article est un résultat analogue dans le cadre des relations d’équivalence boréliennes à classes dénombrables, que nous démontrons en développant une théorie de Bass-Serre dans ce cadre particulier.

We investigate topological AE(0)-groups, a class which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of a universal AE(0)-group of a given weight as well as the existence of a universal action of an AE(0)-group of a given weight on an AE(0)-space of the same weight. A complete characterization of closed subgroups of powers of the symmetric group $S_{\infty }$ is obtained. It is also shown that every AE(0)-group is Baire isomorphic to a product...

We investigate the connections between Ramsey properties of Fraïssé classes and the universal minimal flow $M(G_{)}$ of the automorphism group $G$ of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class has finite Ramsey degree for embeddings, then this degree equals the size of $M(G_{)}$. We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if is a relational Ramsey class and $G$ is amenable, then $M(G_{)}$ admits a unique invariant...

We develop methods for studying transition operators on metric spaces that are invariant under a co-compact group which acts properly. A basic requirement is a decomposition of such operators with respect to the group orbits. We then introduce reduced transition operators on the compact factor space whose norms and spectral radii are upper bounds for the Lp-norms and spectral radii of the original operator. If the group is amenable then the spectral radii of the original and reduced operators coincide,...