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

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

2005-09-22

arxiv.org/abs/math/0509528v1

Theor. and Math. Physics, v. 123, no. 2, 2000, 582--609

Mathematics

Representation Theory

25 pages, LaTeX

Scientific paper

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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