Related papers: Van der Corput's difference theorem for amenable g…

Given a countable discrete amenable group, we study conditions under which a set map into a Banach space (or more generally, a complete semi-normed space) can be realized as the ergodic sum of a vector under a group representation, such…

For any injective von Neumann algebra R and any discrete, countable group G, which acts by *-automorphisms on R, we construct an idempotent mapping of an ultra-weakly dense subspace of B(H) onto the reducerd crossed product von Neumann…

We study fluctuations of ergodic averages generated by actions of amenable groups. In the setting of an abstract ergodic theorem for locally compact second countable amenable groups acting on uniformly convex Banach spaces, we deduce a…

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…

In this paper we discuss some connections between measurable dynamics and rigidity aspects of group representations and group actions. A new ergodic feature of familiar group boundaries is introduced, and is used to obtain rigidity results…

We prove a version of ergodic theorem for an action of an amenable group, where a F{\o} lner sequence needs not to be tempered. Instead, it is assumed that a function satisfies certain mixing condition.

Symbolic dynamical theory plays an important role in the research of amenability with a countable group. Motivated by the deep results of Dougall and Sharp, we study the group extensions for topologically mixing random shifts of finite…

This article shortly provides related proofs of the ergodic theorems of von Neumann, Birkhoff, Wiener, and Rokhlin's lemma for $Z^d$-actions with an invariant measure. It is shown how some deviations of ergodic averages can be structured.…

Generalizing the notion of continuous Hilbert space representations of compact topological groups we define unitary continuous correpresentations of $C^*$-completions of compact quantum group Hopf algebras on arbitrary Hilbert spaces. It is…

The ring of invariant polynomials ${\mathbb C}[V]^G$ over a given finite dimensional representation space $V$ of a complex reductive group $G$ is known, by a famous theorem of Hilbert, to be finitely generated. The general proof being…

We define a metric ultraproduct of topological groups with left-invariant metric, and show that there is a countable sequence of finite groups with left-invariant metric whose metric ultraproduct contains isometrically as a subgroup every…

We define a class of discrete abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

For a finite dimensional representation $V$ of a group $G$ over a field $F$, the degree of reductivity $\delta(G,V)$ is the smallest degree $d$ such that every nonzero fixed point $v\in V^{G}\setminus\{0\}$ can be separated from zero by a…

We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…

In this paper we show that for every congruent monotileable amenable group $G$ and for every metrizable Choquet simplex $K$, there exists a minimal $G$-subshift, which is free on a full measure set, whose set of invariant probability…

The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal…

Given a finite-dimensional faithful representation $V$ of a linearly reductive group $G$ over a field $K=\bar K$, we consider the growth of the number of irreducible factors of $V^{\otimes n}$ when $n$ is large. We prove that there exist…

We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.

We give a new formulation of some of our recent results on the following problem: if all uniformly bounded representations on a discrete group $G$ are similar to unitary ones, is the group amenable? In \S 5, we give a new proof of…