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We consider the most general Dunkl shift operator $L$ with the following properties: (i) $L$ is of first order in the shift operator and involves reflections; (ii) $L$ preserves the space of… (More)

The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is… (More)

- Luc Lapointe, Luc Vinet
- 1996

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with… (More)

The kernel of the Z2 Dirac–Dunkl operator is examined. The symmetry algebra An of the associated Dirac–Dunkl equation on Sn−1 is determined and is seen to correspond to a higher rank generalization… (More)

Abstract:We quantize a compactified version of the trigonometric Ruijsenaars–Schneider particle model with a phase space that is symplectomorphic to the complex projective space ℂℙN. The quantum… (More)

It is shown how to systematically construct the XX quantum spin chains with nearest-neighbor interactions that allow perfect state transfer (PST). Sets of orthogonal polynomials (OPs) are in… (More)

A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations… (More)

The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the… (More)

We study a family of ”classical” orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can… (More)

We introduce a new map from polynomials orthogonal on the unit circle to polynomials orthogonal on the real axis. This map is closely related to the theory of CMV matrices. It contains an arbitrary… (More)