Determinantal construction of orthogonal polynomials associated with root systems

Retrieved October 30, 2007 from http://lanl.arxiv.org/find/math/1/au:+Morse_J/0/1/0/all/0/1We consider semisimple triangular operators acting in the sym- metric component of the group algebra over the weight lattice of a root sys- tem. 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