  We introduce multivariate generalizations of the Bernstein-Szego polynomials,
which are associated to the root systems of the complex simple Lie algebras.
The multivariate polynomials in question generalize Macdonald's Hall-Littlewood
polynomials associated with root systems. For the root system of type A1
(corresponding to the Lie algebra SL (2;C)) the classic Bernstein-Szego
polynomials are recovered.
