Related papers: Factorization and boundedness for representations …

The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. This paper generalises it to arbitrary Lie groups, possibly non-compact. The result relies on knowledge of recoupling…

In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group in terms of representation rings of subgroups of its Sylow. We also prove a stable elements…

We develop the theory of maximal representations of the fundamental group of a compact connected oriented surface with boundary, into a group of Hermitian type. For any such representation we define the Toledo invariant, for which we…

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,…

For any locally compact group $G$, we show the existence and uniqueness up to quasi-equivalence of a unitary $C_0$-representation $\pi_0$ of $G$ such that all coefficient functions of $C_0$-representations of $G$ are coefficient functions…

We define various notions of locality for *-automorphisms of the algebra of observables for an infinitely extended quantum spin system and study their relationship. In particular, we show that the ubiquitous characterization which arises…

We give some natural conditions on actions of discrete countable groups on abelian locally compact groups of Lie type that imply factoriality of the group von Neumann algebras of their semidirect products. This allows us to give a fairly…

We study a particular class of representations from the fundamental groups of punctured spheres $\Sigma_{0,n}$ to the group $\text{PSL} (2,\mathbb R)$ (and their moduli spaces), that we call \emph{super-maximal}. Super-maximal…

Let H be a subgroup of some locally compact group G. Assume H is approximable by discrete subgroups and G admits neighborhood bases which are "almost-invariant" under conjugation by finite subsets of H. Let $m: G \to \mathbb{C}$ be a…

The category of locally compact quantum groups can be described as either Hopf $*$-homomorphisms between universal quantum groups, or as bicharacters on reduced quantum groups. We show how So{\l}tan's quantum Bohr compactification can be…

We show that the space $M_d(G)$ of $M_d$-multipliers of a locally compact group $G$ is isometrically isomorphic to the Banach space of bounded functionals on the $d$-fold Haagerup tensor product of $L^1(G)$ vanishing on the kernel of the…

General semifinite factor representations of the diffeomorphism group of euclidean space are constructed by means of a canonical correspondence with the finite factor representations of the inductive limit unitary group. This construction…

We study finite dimensional representations over some Noetherian algebras over a field of characteristic zero. More precisely, we give necessary and sufficient conditions for the category of locally finite dimensional representations to be…

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…

In this series of papers, we investigate properties of a finite group which are determined by its low degree irreducible representations over a number field $F$, i.e. its representations on matrix rings $\operatorname{M}_n(D)$ with $n \leq…

We prove a strengthening of the Grothendieck-Lefschetz hyperplane theorem for local Picard groups conjectured by Koll\'ar. Our approach, which relies on acyclicity results for absolute integral closures, also leads to a restriction theorem…

For a division ring $D$, denote by $\mathcal M_D$ the $D$-ring obtained as the completion of the direct limit $\varinjlim_n M_{2^n}(D)$ with respect to the metric induced by its unique rank function. We prove that, for any ultramatricial…

We prove that the noncommutative Lorentz norm (associated to a semifinite von Neumann algebra) of a propagator of the form $\varphi(|\mathscr{L}|)$ can be estimated if the modulus of the Borel function $\varphi$ is bounded by a continuous…

We discuss the conical region of convergence of exponential and asymptotically polynomial form factors and their integral representations. Then, we calculate the spectral representation of the propagator of nonlocal theories with entire…

In this article we observe that a locally compact group $G$ is completely determined by the algebraic properties of its Feichtinger's Segal algebra $S_0(G).$ Let $G$ and $H$ be locally compact groups. Then any linear (not necessarily…