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December 2007 Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordon coefficients
Fabio Scarabotti
Methods Appl. Anal. 14(4): 355-386 (December 2007).

Abstract

We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group Sn and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klimyk, we develop a tree-method approach for those intertwining functions. Moreover, using our theory of $S_n$-intertwining functions and James version of the Schur- Weyl duality, we give a proof of the relation between Hahn polynomials and $SU(2)$ Clebsch-Gordan coefficients, previously obtained by Koornwinder and by Nikiforov, Smorodinskiĭ and Suslov in the $SU(2)$-setting. Such relation is also extended to the multidimensional case.

Citation

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Fabio Scarabotti. "Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordon coefficients." Methods Appl. Anal. 14 (4) 355 - 386, December 2007.

Information

Published: December 2007
First available in Project Euclid: 4 November 2008

zbMATH: 1177.33030
MathSciNet: MR2467106

Subjects:
Primary: 33C80
Secondary: 20C30, 33C45, 33C50, 81R05

Rights: Copyright © 2007 International Press of Boston

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Vol.14 • No. 4 • December 2007
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