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

Dimitry Leites·Alexander Sergeev
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Abstract

We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials corresponding to Lie superlagebras. We also describe the real forms of gl(N), quasi-finite modules over gl(N), and conditions for unitarity of the quasi-finite modules. Analogs of tensors over gl(N) are also introduced.

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BibTeXRIS

Dimitry Leites, Alexander Sergeev. 2005-09-22. Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices. https://doi.org/10.1007/bf02551394

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