Related papers: Tame sets in homogeneous spaces

In this paper we give a very simple proof of the existence and plenitude of Runge tubes in $\mathbb C^n$ $(n>1)$ and, more generally, in Stein manifolds with the density property. We show in particular that for any algebraic submanifold $A$…

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…

In this paper we prove the following results: $1)$ We show that any arithmetic quotient of a homogeneous space admits a natural real semi-algebraic structure for which its Hecke correspondences are semi-algebraic. A particularly important…

We introduce abstract net spaces on directed sets and prove their embedding and interpolation properties. Typical examples of interest are lattices of irreducible unitary representations of compact Lie groups and of class I representations…

We prove an analogue of the Oppenheim conjecture for a system comprising an inhomogeneous quadratic form and a linear form in $3$ variables using dynamics on the space of affine lattices.

We show that the group of all holomorphic automorphisms of complex affine space $\mathbb C^n$, $n>1$, and several of its subgroups satisfy the parametric Oka property with approximation and with interpolation on discrete sets.

For any set $A$ of natural numbers with positive upper Banach density and any $k\geq 1$, we show the existence of an infinite set $B\subset{\mathbb N}$ and a shift $t\geq0$ such that $A-t$ contains all sums of $m$ distinct elements from $B$…

We prove an analogue for homogeneous trees and certain affine buildings of a result of Bourgain on pinned distances in sets of positive density in Euclidean spaces. Furthermore, we construct an example of a non-homogeneous tree with…

We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively. After a review of some classical results, we use the Gleason-Iwasawa-Montgomery-Yamabe-Zippin structure…

Let $M$ be a smooth Fano threefold such that a canonical extension of the tangent bundle is an affine manifold. We show that $M$ is rational homogeneous.

Let F be a non-archimedean local field of odd residual characteristic p. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu's construction of complex…

We provide a complete classification of all tame and wild symmetric special multiserial algebras in terms of the underlying Brauer configuration. Our classification contains the symmetric special multiserial algebras of finite…

Here, we classify Lie groups acting isometrically on compact Lorentz manifolds, and in particular we describe the geometric structure of compact homogeneous Lorentz manifolds.

Let $D$ be a bounded homogeneous domain in $\mbb{C}^n$ and let $\Gamma$ be a cyclic discrete subgroup of the automorphism group of $D$. It is shown that the complex space $D/\Gamma$ is Stein.

Let $G$ be a locally compact amenable group. We say that G has property (M) if every closed subgroup of finite covolume in G is cocompact. A classical theorem of Mostow ensures that connected solvable Lie groups have property (M). We prove…

We introduce right amenability, right F{\o}lner nets, and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-F{\o}lner theorem for left homogeneous spaces with finite stabilisers. It states that right…

In order to understand the structure of the cohomologies involved in the study of projectively equivariant quantizations, we introduce a notion of affine representation of a Lie algebra.We show how it is related to linear representations…

We give a criterion for the rigidity of actions on homogeneous spaces. Let $G$ be a real Lie group, $\Lambda$ a lattice in $G$, and $\Gamma$ a subgroup of the affine group Aff$(G)$ stabilizing $\Lambda$. Then the action of $\Gamma$ on…

We construct a map from the classifying space of a discrete Kac-Moody group over the algebraic closure of the field with p elements to the classifying space of a complex topological Kac-Moody group and prove that it is a homology…

We prove a quantitative equidistribution statement for adelic homogeneous subsets whose stabilizer is maximal and semisimple. Fixing the ambient space, the statement is uniform in all parameters. We explain how this implies certain…