Normalized standard intertwining operators associated to an induced representation and its dual (dual in the sense ofAubert) arise in work on a conjecture ofArthur about R-groups. The purpose of this paper is to address the question of relating the normalizing factors used.

In this paper, we introduce a new differential-difference operator Tξ (ξ ∈ R ) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between Tξ and the directional derivative ∂ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this o...

We propose an extension of supersymmetric quantum mechanics which produces a family of isospectral hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given. Further, we show how to build up vector coherent states of the Gazeau-Klauder type associated to our hamiltonians.

The trigonometric KZ equations associated with a Lie algebra g depend on a parameter λ ∈ h where h ⊂ g is the Cartan subalgebra. We suggest a system of dynamical difference equations with respect to λ compatible with the KZ equations. The dynamical equations are constructed in terms of intertwining operators of g -modules.

In this paper, we introduce a new differential-difference operator Tξ (ξ ∈ R ) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between Tξ and the directional derivative ∂ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this o...

We construct representations of the Cuntz algebra O2 from real quadratic transformations of 1-dimensional dynamical systems. By intertwining relations among transformations, we derive relations among operators associated with representations of O2. From these relations, we show properties of these representations.