Related papers: $C^\ast$-blocks and crossed products for classical…

Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and…

A group is irreducibly represented if it has a faithful irreducible unitary representation. For countable groups, a criterion for irreducible representability is given, which generalises a result obtained for finite groups by W. Gasch\"utz…

We establish a "matrix simultaneous diagonalization theorem" for disconnected reductive groups which relaxes both the semisimplicity condition and the commutativity condition. As an application, we prove the following basic results…

The Stable Reduction Theorem guarantees that any smooth, projective, geometrically irreducible curve of genus $g \geq 2$ over a discretely valued field admits a unique stable model after a finite field extension. Computing this model is a…

The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected…

Let $G$ be a connected complex Lie group. A real form of $G$ is a closed subgroup $H\subset G$ whose Lie algebra $\mathfrak{h}$ is a real form of the Lie algebra $\mathfrak{g}$ of $G$. A pair $(G,H)$ of this type is reductive, and the…

Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $\pi$ an irreducible admissible representation of $G$. In this article we prove a necessary and sufficient condition for the finiteness of the multiplicities of $L$-types…

Let $G$ be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of $G$ on $C^*$-algebras $A$ and $B$ are outer conjugate if and only if there is an isomorphism of the crossed products that is…

The notion of a p-adic de Rham representation of the absolute Galois group of a p-adic field was introduced about twenty years ago (see e.g. [Fo93]). Three important results for this theory have been obtained recently: The structure theorem…

W. Paschke's version of Stinespring's theorem associates a Hilbert $C^*$-module along with a generating vector to every completely positive map. Building on this, to every quantum dynamical semigroup (QDS) on a $C^*$-algebra $\mathcal A$…

Let $\mathcal{C}$ be a smooth, projective and geometrically integral curve defined over a finite field $\mathbb{F}$. Let $A$ be the ring of function of $\mathcal{C}$ that are regular outside a closed point $P$ and let $k=\mathrm{Quot}(A)$.…

We introduce the Haagerup property for twisted groupoid $C^*$-dynamical systems in terms of naturally defined positive-definite operator-valued multipliers. By developing a version of `the Haagerup trick' we prove that this property is…

We prove a topological rigidity result for simple, thick, hyperbolic P-manifolds of dimension 2: isomorphism of the fundamental groups implies homeomorphism of the P-manifolds. An immediate application is a diagram rigidity theorem for…

We investigate the irreducible cuspidal $C$-representations of a reductive $p$-adic group $G$ over a field $C$ of characteristic different from $p$. When $C$ is algebraically closed, for many groups $G$, a list of cuspidal $C$-types…

The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…

In the seventies, V. G. Drinfeld proved that a moduli problem of deformations by quasi-isogenies of certain $p$-divisible groups with extra actions is representable by an explicit semi-stable model of the $p$-adic symmetric space. This…

The purpose of this paper is construct an embedding of the C*-algebra of the Cartan motion group of a real reductive group G into the reduced C*-algebra of G itself. The embedding has a number of applications: we shall use it to…

Let $\pi $ be an irreducible smooth complex representation of a general linear $p$-adic group and let $\sigma $ be an irreducible complex supercuspidal representation of a classical $p$-adic group of a given type, so that $\pi\otimes\sigma…

We give a geometric account of Harish-Chandra's principle that a tempered irreducible representation of a real reductive group is either square-integrable modulo center, or embeddable in a representation that is parabolically induced from…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…