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Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these polynomials are provided. The domain of validity for the indices and variables of these polynomials is also determined. Particular limits on the parameters entering the polynomials allow to define several Griffiths polynomials of other types. One special limit connects them to the original Griffiths polynomials (of Krawtchouk type). Finally, a connection with the 9j symbols is made. [ABSTRACT FROM AUTHOR]

We compute the matrix elements of SO(3) in any finite-dimensional irreducible representation of sl3. They are expressed in terms of a double sum of products of Krawtchouk and Racah polynomials which generalize the Griffiths–Krawtchouk polynomials. Their recurrence and difference relations are obtained as byproducts of our construction. The proof is based on the decomposition of a general three-dimensional rotation in terms of elementary planar rotations and a transition between two embeddings of sl2 in sl3. The former is related to monovariate Krawtchouk polynomials and the latter, to monovariate Racah polynomials. The appearance of Racah polynomials in this context is algebraically explained by showing that the two sl2 Casimir elements related to the two embeddings of sl2 in sl3 obey the Racah algebra relations. We also show that these two elements generate the centralizer in U(sl3) of the Cartan subalgebra and its complete algebraic description is given. [ABSTRACT FROM AUTHOR]

Free fermions on Johnson graphs J(n, k) are considered, and the entanglement entropy of sets of neighborhoods is computed. For a subsystem composed of a single neighborhood, an analytical expression is provided by the decomposition in irreducible submodules of the Terwilliger algebra of J(n, k) embedded in two copies of s u (2). For a subsystem composed of multiple neighborhoods, the construction of a block-tridiagonal operator that commutes with the entanglement Hamiltonian is presented, its usefulness in computing the entropy is stressed, and the area law pre-factor is discussed. [ABSTRACT FROM AUTHOR]

It is shown that the tridiagonalization of the hypergeometric operator L yields the generic Heun operator M. The algebra generated by the operators L,M and Z = [L,M] is quadratic and a one-parameter generalization of the Racah algebra. The Racah-Heun orthogonal polynomials are introduced as overlap coefficients between the eigenfunctions of the operators L and M. An interpretation in terms of the Racah problem for su(1,1) and separation of variables in a superintegrable system are discussed. [ABSTRACT FROM AUTHOR]

Studies the discretization of the Helmholtz, heat and wave equations on uniform lattices in various space-time dimensions. Symmetry properties of finite-difference equations; Solutions with definite transformation properties; Identities and formulas for the functions derived using symmetry algebra.

A supermultiplet of two spin-0 and one spin- 1/2 particle in a Coulomb potential has been shown recently to possess a dynamical OSp(2,1) symmetry algebra. The canonical chain of maximal subalgebras leads to a natural choice of quantum numbers and state vectors. The relevant representations of OSp(2,1) are constructed in this adapted basis, and the wave functions subsequently obtained by going to a coordinate realization. [ABSTRACT FROM AUTHOR]

This work is concerned with the characterization of field supermultiplets on four-dimensional Minkowski space that are stable under the action of subgroups of the superconformal group SU(2,2/1). The most general scalar and vector superfields whose Lie derivative with respect to a fermionic tangent vector vanishes are determined. Invariance under subgroups of SU(2,2/1) with more than one odd generator is also discussed. [ABSTRACT FROM AUTHOR]

The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl-1(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from the q → -1 limit of the dual q-Hahn polynomials. The Hopf algebra sl-1(2) has four generators including an involution, it is also a q → -1 limit of the quantum algebra slq(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter generalization of u(2) with an involution as additional generator, is first derived from the recurrence relation of the -1 Hahn polynomials. It is then shown that H can be realized in terms of the generators of two added sl-1(2) algebras, so that the Clebsch-Gordan coefficients of sl-1(2) are dual -1 Hahn polynomials. An irreducible representation of H involving five-diagonal matrices and connected to the difference equation of the dual -1 Hahn polynomials is constructed. [ABSTRACT FROM AUTHOR]