Related papers: The Howe-Moore property for real and p-adic groups

The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the signature of the associated hermitian form. In this article, this theorem is generalized to…

In this article we prove some previously announced results about metric ultraproducts of finite simple groups. We show that any non-discrete metric ultraproduct of alternating or special linear groups is a geodesic metric space. For more…

For the group of endo-permutation modules of a finite \(p\)-group, there is a surjective reduction modulo \(p\) homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic \(p\). We prove…

The aim of this paper is to prove ergodic decomposition theorems for probability measures quasi-invariant under Borel actions of inductively compact groups (Theorem 1) as well as for sigma-finite invariant measures (Corollary 1). For…

We develop the theory of Patterson-Sullivan measures on the boundary of a locally compact hyperbolic group, associating to certain left invariant metrics on the group measures on the boundary. We later prove that for second countable,…

Let us call pseudo-homothetic group the non-unimodular 3-dimensional Lie group that is the semi-direct product of $\mathbb{R}$ acting non-semisimply on $\mathbb{R}^2$. In this article, we solve the geodesic completeness problem on this Lie…

If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism…

A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measurable cochains. That theory was shown to enjoy analogs of most of the standard algebraic…

We consider the class of groups called identity excluding which has the property that any non-trivial irreducible unitary representation restricted to a dense subgroup does not weakly contain the trivial representation. For adapted and…

We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform \pi_0 we prove an exact relation between…

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

Wright showed that, if a 1-ended simply connected locally compact ANR Y with pro-monomorphic fundamental group at infinity admits a proper Z-action, then that fundamental group at infinity can be represented by an inverse sequence of…

We study the following question: given a locally compact group when does its Fourier algebra coincide with the subalgebra of the Fourier-Stieltjes algebra consisting of functions vanishing at infinity? We provide sufficient conditions for…

We show that the geometric and homological finiteness properties of group pairs are invariant under a suitable notion of quasi-isometry for group pairs.

I will survey some results in the theory of modular representations of a reductive $p$-adic group, in positive characteristic $\ell \neq p$ and $\ell=p$.

We compute the equivariant complex K-theory ring of a cohomogeneity-one action of a compact Lie group at the level of generators and relations and derive a characterization of K-theoretic equivariant formality for these actions. Less…

We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of…

Let $\rho_0$ be an action of a Lie group on a manifold with boundary that is transitive on the interior. We study the set of actions that are topologically conjugate to $\rho_0$, up to smooth or analytic change of coordinates. We show that…

A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie…

We use a Mayer-Vietoris-like spectral sequence to establish vanishing results for the cohomology of complements of linear and elliptic hyperplane arrangements, as part of a more general framework involving duality and abelian duality…