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.
Publié le : 2007-12-15
Classification:
Hahn polynomials,
intertwining functions,
tree method,
symmetric group,
special unitary group,
Clebsch-Gordan coefficients,
$3nj$-coefficients,
33C80,
20C30,
33C45,
33C50,
81R05
@article{1225813982,
author = {Scarabotti, Fabio},
title = {Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordon coefficients},
journal = {Methods Appl. Anal.},
volume = {14},
number = {1},
year = {2007},
pages = { 355-386},
language = {en},
url = {http://dml.mathdoc.fr/item/1225813982}
}
Scarabotti, Fabio. Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordon coefficients. Methods Appl. Anal., Tome 14 (2007) no. 1, pp. 355-386. http://gdmltest.u-ga.fr/item/1225813982/