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This article is cited in 12 scientific papers (total 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.
Citation:
D. A. Leites, A. N. Sergeev, “Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices”, TMF, 123:2 (2000), 205–236; Theoret. and Math. Phys., 123:2 (2000), 582–608
Linking options:
https://www.mathnet.ru/eng/tmf599https://doi.org/10.4213/tmf599 https://www.mathnet.ru/eng/tmf/v123/i2/p205
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Abstract page: | 531 | Full-text PDF : | 250 | References: | 60 | First page: | 1 |
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