42 citations · 585 across the 52 of their papers we have counts for
52 papers
Impact of the non-canonical approach to the exact solution of the ideal one-dimensional electron gas confined with an anisotropic quantum wire of oscillator-shaped profile
E. I. Jafarov, S. M. Nagiyev, J. Van der Jeugt
We study an exactly solvable model that can be interpreted as an ideal one-dimensional electron gas confined with an anisotropic quantum wire potential of oscillator-shaped profile…
Graded Casimir Elements and Central Extensions of Color Lie Algebras
Naruhiko Aizawa, Ichi Fujii, Jambulingam Segar +1
A color Lie algebra is a generalization of a Lie (super)algebra by an Abelian group . The underlying vector space and defining relations of the algebra are graded by , and a…
Orthosymplectic -graded Lie superalgebras and parastatistics
N. I. Stoilova, J. Van der Jeugt
A -graded Lie superalgebra is a -graded algebra with a bracket that satisfies certain graded versions of the symmetry and Jacobi identity.…
On classical -graded Lie algebras
N. I. Stoilova, J. Van der Jeugt
We construct classes of -graded Lie algebras corresponding to the classical Lie algebras, in terms of their defining matrices. For the -graded Lie a…
The exceptional Lie algebra generated by three generators subject to quadruple relations
N. I. Stoilova, J. Van der Jeugt
In this short communication we show how the Lie algebra can easily be described as a free Lie algebra on 3 generators, subject to some simple quadruple relations f…
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…
Bases for infinite dimensional simple -modules respecting the branching
Asmus K. Bisbo, Joris Van der Jeugt
We study the effects of the branching on a particular class of simple infinite-dimensional -modules char…
A Klein operator for paraparticles
N. I. Stoilova, J. Van der Jeugt
It has been known for a long time that there are two non-trivial possibilities for the relative commutation relations between a set of parafermions and a set of parabosons.…
The -graded Lie superalgebras and , and parastatistics Fock spaces
N. I. Stoilova, J. Van der Jeugt
The parastatistics Fock spaces of order corresponding to an infinite number of parafermions and parabosons with relative paraboson relations are constructed. The Fock spaces ar…
The Z_2 x Z_2-graded Lie superalgebra pso(2m+1|2n) and new parastatistics representations
N. I. Stoilova, J. Van der Jeugt
When the relative commutation relations between a set of m parafermions and n parabosons are of ``relative parafermion type'', the underlying algebraic structure is the classical o…
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 quantum oscillator model related to special sets of Racah polynomials
Roy Oste, Joris Van der Jeugt
In Oste and Van der Jeugt, SIGMA, 12 (2016) we classified all pairs of recurrence relations in which two (dual) Hahn polynomials with different parameters appear. Such pairs are re…
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…
Extension of the osp(m|n)~ so(m-n) Correspondence to the Infinite-Dimensional Chiral Spinors and Self Dual Tensors
N. I. Stoilova, J. Thierry-Mieg, J. Van der Jeugt
The spinor representations of the orthosymplectic Lie superalgebras osp(m|n) are considered and constructed. These are infinite-dimensional irreducible representations, of which th…
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…
On a pair of difference equations for the type orthogonal polynomials and related exactly-solvable quantum systems
E. I. Jafarov, N. I. Stoilova, J. Van der Jeugt
We introduce a pair of novel difference equations, whose solutions are expressed in terms of Racah or Wilson polynomials depending on the nature of the finite-difference step. A nu…
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…
A Wigner distribution function for finite oscillator systems
Joris Van der Jeugt
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The d…
The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials
E. I. Jafarov, J. Van der Jeugt
We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg-Weyl superalgebra or "the algebra of supersymmetric qu…
A finite oscillator model related to sl(2|1)
E. I. Jafarov, J. Van der Jeugt
We investigate a new model for the finite one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). In this setting, it is natural to present the position and mom…
Deformed su(1,1) Algebra as a Model for Quantum Oscillators
Elchin I. Jafarov, Neli I. Stoilova, Joris Van der Jeugt
The Lie algebra can be deformed by a reflection operator, in such a way that the positive discrete series representations of can be extend…
Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator
Gilles Regniers, Joris Van der Jeugt
In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and th…