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math.RT2019
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…
math.RT2019
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.…
math.RT2019
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(…