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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 123, Number 2, Pages 205–236
DOI: https://doi.org/10.4213/tmf599
(Mi tmf599)
 

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
References:
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.
English version:
Theoretical and Mathematical Physics, 2000, Volume 123, Issue 2, Pages 582–608
DOI: https://doi.org/10.1007/BF02551394
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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\paper Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices
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\jour Theoret. and Math. Phys.
\yr 2000
\vol 123
\issue 2
\pages 582--608
\crossref{https://doi.org/10.1007/BF02551394}
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Linking options:
  • https://www.mathnet.ru/eng/tmf599
  • https://doi.org/10.4213/tmf599
  • https://www.mathnet.ru/eng/tmf/v123/i2/p205
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:539
    Full-text PDF :256
    References:65
    First page:1
     
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