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Bargmann and Barut-Girardello models for the Racah algebra
Hendrik De Bie, Plamen Iliev, Luc Vinet
The Racah algebra and its higher rank extension are the algebras underlying the univariate and multivariate Racah polynomials. In this paper we develop two new models in which the…
corepresentations and bivariate -Krawtchouk polynomials
Geoffroy Bergeron, Erik Koelink, Luc Vinet
The matrix elements of unitary corepresentations, which are analogues of the symmetric powers of the natural repesentation, are shown to be the bivariate -Krawtchouk o…
The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type
Pascal Baseilhac, Satoshi Tsujimoto, Luc Vinet +1
The Heun-Askey-Wilson algebra is introduced through generators $\{\boX,\boW\}$ and relations. These relations can be understood as an extension of the usual Askey-Wilson ones. A ce…
The Higgs and Hahn algebras from a Howe duality perspective
Luc Frappat, Julien Gaboriaud, Luc Vinet +2
The Hahn algebra encodes the bispectral properties of the eponymous orthogonal polynomials. In the discrete case, it is isomorphic to the polynomial algebra identified by Higgs as…
The dual pair , the Dirac equation and the Bannai-Ito algebra
Julien Gaboriaud, Luc Vinet, Stéphane Vinet +1
The Bannai-Ito algebra can be defined as the centralizer of the coproduct embedding of in . It will be shown that it is also…
The generalized Racah algebra as a commutant
Julien Gaboriaud, Luc Vinet, Stéphane Vinet +1
The Racah algebra of rank is obtained as the commutant of the \mbox{} subalgebra of in oscillator representations of t…