29 citations · 120 across the 16 of their papers we have counts for
16 papers
On angular momentum algebras and their relations
Kieran Calvert, Marcelo De Martino, Roy Oste
In this paper, we study the centraliser of , denoted the total angular momentum algebra (TAMA), in the Weyl Clifford algebra. The TAMA extends the angular mome…
The double dihedral Dunkl total angular momentum algebra
Marcelo De Martino, Alexis Langlois-Rémillard, Roy Oste
The Dunkl total angular momentum algebra (TAMA) is realised as the dual partner of the orthosymplectic Lie superalgebra containing the Dunkl deformation of the Dirac operator. In t…
The centre of the Dunkl total angular momentum algebra
Kieran Calvert, Marcelo De Martino, Roy Oste
For a finite dimensional representation of a finite reflection group , we consider the rational Cherednik algebra associated with at the para…
Generalised symmetries and bases for Dunkl monogenics
Hendrik De Bie, Alexis Langlois-Rémillard, Roy Oste +1
We introduce a family of commuting generalised symmetries of the Dunkl--Dirac operator inspired by the Maxwell construction in harmonic analysis. We use these generalised symmetrie…
Supercentralizers for deformations of the Pin osp dual pair
Roy Oste
In recent work, we examined the algebraic structure underlying a class of elements supercommuting with realization of the Lie superalgebra inside a generaliza…
Exact solution of the position-dependent effective mass and angular frequency Schrödinger equation: harmonic oscillator model with quantized confinement parameter
E. I. Jafarov, S. M. Nagiyev, R. Oste +1
We present an exact solution of a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the positi…
Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl--Dirac operator
Hendrik De Bie, Alexis Langlois-Rémillard, Roy Oste +1
The Dunkl--Dirac operator is a deformation of the Dirac operator by means of Dunkl derivatives. We investigate the symmetry algebra generated by the elements supercommuting with th…
An exceptional symmetry algebra for the 3D Dirac-Dunkl operator
Alexis Langlois-Rémillard, Roy Oste
We initiate the study of an algebra of symmetries for the 3D Dirac-Dunkl operator associated with the Weyl group of the exceptional root system . For this symmetry algebra, we…
Deformations of unitary Howe dual pairs
Dan Ciubotaru, Hendrik De Bie, Marcelo De Martino +1
We study deformations of the Howe dual pairs and to the context of a rational Cherednik algebra $H_{1,c}(G,E…
The total angular momentum algebra related to the Dunkl Dirac equation
Hendrik De Bie, Roy Oste, Joris Van der Jeugt
We consider the symmetry algebra generated by the total angular momentum operators, appearing as constants of motion of the Dunkl Dirac equation. The latter is a def…
On the algebra of symmetries of Laplace and Dirac operators
Hendrik De Bie, Roy Oste, Joris Van der Jeugt
We consider a generalization of the classical Laplace operator, which includes the Laplace-Dunkl operator defined in terms of the differential-difference operators associated with…
A finite oscillator model with equidistant position spectrum based on an extension of
Roy Oste, Joris Van der Jeugt
We consider an extension of the real Lie algebra by introducing a parity operator and a parameter . This extended algebra is isomorphic to the Bannai-Ito…
The Wigner distribution function for the finite oscillator and Dyck paths
Roy Oste, Joris Van der Jeugt
Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-…
Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix
Roy Oste, Joris Van der Jeugt
The Clement or Sylvester-Kac matrix is a tridiagonal matrix with zero diagonal and simple integer entries. Its spectrum is known explicitly and consists of integers which makes it…
Doubling (Dual) Hahn Polynomials: Classification and Applications
Roy Oste, Joris Van der Jeugt
We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The…
Generalized Fourier transforms arising from the enveloping algebras of sl(2) and osp(1|2)
H. De Bie, R. Oste, J. Van der Jeugt
The Howe dual pair (sl(2),O(m)) allows the characterization of the classical Fourier transform (FT) on the space of rapidly decreasing functions as the exponential of a well-chosen…