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Determinantal Construction of Orthogonal Polynomials Associated with Root Systems

Jan Felipe van Diejen·Luc Lapointe·Jennifer Morse
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Abstract

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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Jan Felipe van Diejen, Luc Lapointe, Jennifer Morse. 2003-03-20. Determinantal Construction of Orthogonal Polynomials Associated with Root Systems. https://doi.org/10.1112/s0010437x03000149

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