Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordan coefficients

Details Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordan coefficients Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordan coefficients

2008-05-06

arxiv.org/abs/0805.0670v1

Methods Appl. Anal. 14 (2007), no. 4, 355-386 (2008)

Mathematics

Classical Analysis and ODEs

31 pages, 4 figures

Scientific paper

We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klymik, we develop a tree-method approach for those intertwining functions. We also give a group theoretic proof of the relation between Hahn polynomials and Clebesh-Gordan coefficients, given analytically by Koornwinder and by Nikiforov, Smorodinski\u{i} and Suslov. Such relation is also extended to the multidimensional case.

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