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arXiv · 0805.0670

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

Fabio Scarabotti
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Abstract

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, Smorodinskiĭ and Suslov. Such relation is also extended to the multidimensional case.

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Fabio Scarabotti. 2008-05-06. Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordan coefficients. https://arxiv.org/abs/0805.0670

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