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…
symmetry of XX spin chains
Nicolas Crampé, Rafael I. Nepomechie, Luc Vinet +1
We show that, after suitably adjusting a uniform transverse magnetic field, the generic inhomogeneous open XX spin chain has a two-fold degeneracy, and an exact symmetry wh…
Algebras behind the bispectrality of the Wilson rational functions and their limits
Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet +1
The properties of the Wilson rational functions with three different normalizations are described. For one normalization, it satisfies an recurrence relation,…