Abstract

We introduce multivariate generalizations of the Bernstein-Szegö 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 l (2; )) the classic Bernstein-Szegö polynomials are recovered. © 2007 London Mathematical Society.