arXiv math/05095282005-09-22math.RT

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

Dimitry Leites, Alexander Sergeev

备注：: 25 pages, LaTeX
发表信息：: Theor. and Math. Physics, v. 123, no. 2, 2000, 582--609
DOI：: 10.1007/BF02551394

英文摘要：

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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