Bernstein-Szegö polynomials associated with root systems. (English) Zbl 1126.05101
Summary: 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 \(A_{1}\) (corresponding to the Lie algebra \(\mathfrak {sl} (2; \mathbb C))\) the classic Bernstein-Szegö polynomials are recovered.
MSC:
05E05 | Symmetric functions and generalizations |
05E35 | Orthogonal polynomials (combinatorics) (MSC2000) |
33D52 | Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) |