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

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 gl(lambda) for lambda is an element of 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 gl(lambda), real forms of this algebra, anti the unitary conditions for quasi-finite modules. Analogues of tensors over gl(lambda) are also introduced.