Determinantal Construction of Orthogonal Polynomials Associated with Root Systems

Details Determinantal Construction of Orthogonal Polynomials Associated with Root Systems Determinantal Construction of Orthogonal Polynomials Associated with Root Systems

2003-03-20

arxiv.org/abs/math/0303263v1

Compositio Math, 140/2, 255--273 (2004)

Mathematics

Combinatorics

28 pages

Scientific paper

10.1112/S0010437X03000149

We consider semisimple triangular operators acting in the symmetric component
of the group algebra over the weight lattice of a root system. We present a
determinantal formula for the eigenbasis of such triangular operators. This
determinantal formula gives rise to an explicit construction of the Macdonald
polynomials and of the Heckman-Opdam generalized Jacobi polynomials.

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