Related papers: Weak containment of representation on topological …

We study the natural representation of the topological full group of an ample Hausdorff groupoid in the groupoid's complex Steinberg algebra and in its full and reduced C*-algebras. We characterise precisely when this representation is…

The induced representation ${\rm Ind}_H^GS$ of a locally compact group $G$ is the unitary representation of the group $G$ associated with unitary representation $S:H\rightarrow U(V)$ of a subgroup $H$ of the group $G$. Our aim is to develop…

We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects and discuss some of the standard constructions from representation theory in this…

If A is a weak C^*-Hopf algebra then the category of finite dimensional unitary representations of A is a monoidal C^*-category with monoidal unit being the GNS representation D_eps associated to the counit \eps. This category has…

A uniformly continuously integrable sequence of real-valued measurable functions, defined on some probability space, is relatively compact in the $\sigma(L^1,L^\infty)$ topology. In this paper, we link such a result to weak convergence…

We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We proceed to provide…

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…

In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type…

Let $G$ be a locally compact abelian group with Pontraygin dual $\widehat{G}$. Suppose $P$ is a closed subsemigroup of $G$ containing the identity element $0$. We assume that $P$ has dense interior and $P$ generates $G$. Let…

Let $G$ and $T$ be topological groups, $\alpha : T \to \Aut(G)$ a homomorphism defining a continuous action of $T$ on $G$ and $G^\sharp := G \rtimes_\alpha T$ the corresponding semidirect product group. In this paper we address several…

Suppose that $G$ is a locally compact group and $\pi$ is a (not necessarily irreducible) unitary representation of a closed normal subgroup $N$ of $G$ on a Hilbert space $H$. We extend results of Clifford and Mackey to determine when $\pi$…

The aim of this paper is to introduce and to investigate the analogues of torsors for compact quantum groups and to study their role in representation theory. Let A be a unitarizable Hopf *-algebra: we show that there is a category…

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 any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a "universal" hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in…

We show that if $H \leq G$ is a closed amenable and cocompact subgroup of a unimodular locally compact group, then the reduced group C*-algebra of $G$ is not simple. Equivalently, there are unitary representations of $G$ that are weakly…

In this paper we investigate relations between Koopman, groupoid and quasi-regular representations of countable groups. We show that for an ergodic measure class preserving action of a countable group G on a standard Borel space the…

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 lack of a $p$-adic Haar measure causes many methods of traditional representation theory to break down when applied to continuous representations of a compact $p$-adic Lie group $G$ in Banach spaces over a given $p$-adic field $K$. For…

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…

We consider topological groupoids in finite and also in a compact settings. In the initial sections, we introduce definitions of typical observables and we studied them in the context of statistical mechanics and quantum mechanics. We…