In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

‎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 ...

In this paper, we define the Schrödinger-Weil representation for the Jacobi group and construct covariant maps for the Schrödinger-Weil representation. Using these covariant maps, we construct Jacobi forms with respect to an arithmetic subgroup of the Jacobi group.

Let φ be an isometric automorphism of the non-commutative disc algebra An for n ≥ 2. We show that every contractive covariant representation of (An, φ) dilates to a unitary covariant representation of (On, φ). Hence the C*-envelope of the semicrossed product An ×φ Z is On ×φ Z.

Covariant tensor representations of glm|n occur as irreducible components of tensor powers of the natural (m + n)-dimensional representation. We construct a basis of each covariant representation and give explicit formulas for the action of the generators of glm|n in this basis. The basis has the property that the natural Lie subalgebras glm and gln act by the classical Gelfand–Tsetlin formulas...