Bernstein-Szego Polynomials Associated with Root Systems

Abstract

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.

LaTeX, 12 pages

Cited by in corpus (3)

• Orthogonal polynomials of compact simple Lie groups
• Exact cubature rules for symmetric functions
• On a two variable class of Bernstein-Szego measures