45 citations · 343 across the 47 of their papers we have counts for
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Racah problems for the oscillator algebra, the Lie algebra , and multivariate Krawtchouk polynomials
Nicolas Crampé, Wouter van de Vijver, Luc Vinet
The oscillator Racah algebra is realized by the intermediate Casimir operators arising in the multifold tensor product of the oscillator algebra $\mat…
Revisiting the Askey--Wilson algebra with the universal R-matrix of
Nicolas Crampe, Julien Gaboriaud, Luc Vinet +1
A description of the embedding of the universal Askey--Wilson algebra, AW(3), in is given in terms of the universal R-matrix of . The generators…
Bannai-Ito algebras and the universal R-matrix of osp(1|2)
Nicolas Crampe, Luc Vinet, Meri Zaimi
The Bannai-Ito algebra is viewed as the centralizer of the action of in the -fold tensor product of the universal algebra of this Lie superalgebra.…
Free-Fermion entanglement and orthogonal polynomials
Nicolas Crampé, Rafael I. Nepomechie, Luc Vinet
We present a simple construction for a tridiagonal matrix that commutes with the hopping matrix for the entanglement Hamiltonian of open finite free-Fermion chains a…
Centralizers of the superalgebra osp(1|2): the Brauer algebra as a quotient of the Bannai-Ito algebra
Nicolas Crampe, Luc Frappat, Luc Vinet
We provide an explicit isomorphism between a quotient of the Bannai--Ito algebra and the Brauer algebra. We clarify also the connection with the action of the Lie superalgebra osp(…
Temperley-Lieb, Brauer and Racah algebras and other centralizers of su(2)
Nicolas Crampe, Loïc Poulain d'Andecy, Luc Vinet
In the spirit of the Schur-Weyl duality, we study the connections between the Racah algebra and the centralizers of tensor products of three (possibly different) irreducible repres…
sigma models described through hypergeometric orthogonal polynomials
N. Crampe, A. M. Grundland
The main objective of this paper is to establish a new connection between the Hermitian rank-1 projector solutions of the Euclidean sigma model in two dimensions…
Heun algebras of Lie type
Nicolas Crampé, Luc Vinet, Alexei Zhedanov
We introduce Heun algebras of Lie type. They are obtained from bispectral pairs associated to simple or solvable Lie algebras of dimension three or four. For , th…
Truncation of the reflection algebra and the Hahn algebra
Nicolas Crampe, Eric Ragoucy, Luc Vinet +1
In the context of connections between algebras coming from quantum integrable systems and algebras associated to the orthogonal polynomials of the Askey scheme, we prove that the t…