6 papers
Realization embeddings of the rank two Racah algebra into the rank two Jacobi algebra
Nicolas Crampé, Sarah Post, Luc Vinet
We construct an explicit embedding of the rank two Racah algebra into the rank two Jacobi algebra . Working in the differential model of $\mathfrak…
The quantum loop algebra of and -Racah type bivariate functions
Pascal Baseilhac, Nicolas Crampe
A unified algebraic framework for two different six-parameter families of bivariate -Racah type functions is given using the representation theory of the quantum loop algebra $\…
Polynomials of the Askey Scheme as Clebsch-Gordan Coefficients
Nicolas Crampé, Loïc Poulain d'Andecy, Luc Vinet
Given a semi-simple algebra equipped with a coproduct, the Clebsch-Gordan coefficients are the elements of the transition matrices between direct product representation and its irr…
Perfect state transfer in inhomogeneous XX model of q-Racah type
Nicolas Crampe, Simon Lafrance, Charles Robillard +1
New exactly solvable one-dimensional XX spin chain models that exhibit perfect state transfer are defined. These models have inhomogeneous couplings and magnetic fields determined…
The rank two Jacobi algebra
Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet +1
The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is s…
Change of basis for the tridiagonal pairs of type II
Nicolas Crampe, Julien Gaboriaud, Satoshi Tsujimoto
We study tridiagonal pairs of type II. These involve two linear transformations and . We define two bases. In the first one, acts as a diagonal matrix while $A^\st…