Geodesic
Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 2, pp. 205-236 
D. A. Leites; A. N. Sergeev. Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 2, pp. 205-236. http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We give a uniform interpretation of the classical continuous Chebyshev and Hahn orthogonal polynomials of a discrete variable in terms of the Feigin Lie algebra $\mathfrak{gl}(\lambda)$ for $\lambda\in\mathbb C$. The Chebyshev and Hahn $q$-polynomials admit a similar interpretation, and orthogonal polynomials corresponding to Lie superalgebras can be introduced. We also describe quasi-finite modules over $\mathfrak{gl}(\lambda)$, real forms of this algebra, and the unitarity conditions for quasi-finite modules. Analogues of tensors over $\mathfrak{gl}(\lambda)$ are also introduced.

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