Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordan coefficients
Classical Analysis and ODEs
2011-01-11 v1 Representation Theory
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, Smorodinski\u{i} and Suslov. Such relation is also extended to the multidimensional case.
Cite
@article{arxiv.0805.0670,
title = {Multidimensional Hahn polynomials, intertwining functions on the symmetric group and Clebsch-Gordan coefficients},
author = {Fabio Scarabotti},
journal= {arXiv preprint arXiv:0805.0670},
year = {2011}
}
Comments
31 pages, 4 figures