42 citations · 585 across the 52 of their papers we have counts for
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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…
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…
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…
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…
The su(2)_α Hahn oscillator and a discrete Hahn-Fourier transform
E. I. Jafarov, N. I. Stoilova, J. Van der Jeugt
We define the quadratic algebra su(2)_α which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (w…
Finite oscillator models: the Hahn oscillator
E. I. Jafarov, N. I. Stoilova, J. Van der Jeugt
A new model for the finite one-dimensional harmonic oscillator is proposed based upon the algebra u(2)_α. This algebra is a deformation of the Lie algebra u(2) extended by a parity…
An Exactly Solvable Spin Chain Related to Hahn Polynomials
Neli I. Stoilova, Joris Van der Jeugt
We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter and d…
Wigner quantization of some one-dimensional Hamiltonians
Gilles Regniers, Joris Van der Jeugt
Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have bee…
Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)
N. I. Stoilova, J. Van der Jeugt
A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie super…
The Hamiltonian H=xp and classification of osp(1|2) representations
G. Regniers, J. Van der Jeugt
The quantization of the simple one-dimensional Hamiltonian H=xp is of interest for its mathematical properties rather than for its physical relevance. In fact, the Berry-Keating co…
Solutions of the compatibility conditions for a Wigner quantum oscillator
N. I. Stoilova, J. Van der Jeugt
We consider the compatibility conditions for a N-particle D-dimensional Wigner quantum oscillator. These conditions can be rewritten as certain triple relations involving anticommu…
Realizations of the Lie superalgebra q(2) and applications
N. Debergh, J. Van der Jeugt
The Lie superalgebra q(2) and its class of irreducible representations V_p of dimension 2p (p being a positive integer) are considered. The action of the q(2) generators on a basis…
Fock representations of the superalgebra sl(n+1|m), its quantum analogue U_q[sl(n+1|m)] and related quantum statistics
T. D. Palev, N. I. Stoilova, J. Van der Jeugt
Fock space representations of the Lie superalgebra and of its quantum analogue are written down. The results are based on a description of these supera…