Bernstein-Szego Polynomials Associated with Root Systems

Mathematics – Combinatorics

Scientific paper

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LaTeX, 12 pages

Scientific paper

10.1112/blms/bdm073

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.

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