‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices of a unitary representation to canonical form, give a certain description of the representations of canonical form, and reduce the problem of classifying Eu...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...

The irreducible unitary representations of GL(n, ~) have been classified by D. Vogan in [V2]. In his work, four families of representations play a special role. They are (i) the one dimensional unitary representations and (ii) their complementary series; (iii) Speh's representations and (iv) their complementary series. These representations serve as "building blocks" in the sense that every irr...