4 papers
Bispectral rational functions and Leonard trios
Nicolas Crampé, Wolter Groenevelt, Quentin Labriet +3
It is well-known that Leonard pairs have a close connection with bispectral orthogonal polynomials of the Askey scheme. In this paper, we introduce the notion of a Leonard trio $(V…
Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is used to provide an interpretation of the two-variable Jacobi polynomials on the triangle, as overlaps betwee…
Exactly solvable inhomogeneous XY spin chain
Pierre-Antoine Bernard, Nicolas Crampé, Quentin Labriet +2
Analytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jorda…
Contiguity relations for finite families of orthogonal polynomials in the Askey scheme
Nicolas Crampé, Lucia Morey, Luc Vinet +1
This paper classifies the contiguity relations for finite families of polynomials within the (-)Askey scheme. The necessary and sufficient conditions for the existence of these…