Discriminants and functional equations for polynomials orthogonal on the unit circle

We derive raising and lowering operators fbr orthogonal polynomials on the unit circle and find second order differential and q-difference equations f or these polynomials. A general functional equation is found which allows o ne to relate the zeros of the orthogonal polynomials to the stationary valu es of an explicit quasi-energy and implies recurrences on the orthogonal po lynomial coefficients. We also evaluate the discriminants and quantized dis criminants of polynomials orthogonal on the unit circle. (C) 2001 Academic Press.