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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2000 Volume 123, Number 2, Pages 205–236 (Mi tmf599)

This article is cited in 12 papers

Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices

D. A. Leitesa, A. N. Sergeevb

a Stockholm University
b Balakovo Institute of Technique, Technology and Control

Abstract: 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.

DOI: 10.4213/tmf599


 English version:
Theoretical and Mathematical Physics, 2000, 123:2, 582–608

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© Steklov Math. Inst. of RAS, 2025