Orthogonal polynomials of discrete variable and Lie algebras of complex   size matrices
  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. 
Dimitry Leites, Alexander Sergeev