72 citations · 524 across the 41 of their papers we have counts for
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Gaudin models for some classical multivariate distributions
Plamen Iliev
Representations of the Kohno-Drinfeld Lie algebra associated with several classical multivariate distributions have played an important role in recent developments in the theory of…
Superspace realizations of the Bannai-Ito algebra
N. Crampe, H. De Bie, P. Iliev +1
A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra in te…
Gaudin model for the multinomial distribution
Plamen Iliev
The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno-Drinfeld Lie algebra associated with the multinomial distribution. The main result i…
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…
Symmetry algebra for the generic superintegrable system on the sphere
Plamen Iliev
The goal of the present paper is to provide a detailed study of irreducible representations of the algebra generated by the symmetries of the generic quantum superintegrable system…
The generic quantum superintegrable system on the sphere and Racah operators
Plamen Iliev
We consider the generic quantum superintegrable system on the -sphere with potential , where are parameters. Appropriately normaliz…