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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 969424, 23 pages
http://dx.doi.org/10.1155/2011/969424
Research Article

Orthogonal Polynomials of Compact Simple Lie Groups

1Department of Applied Research, Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Street, Kyiv-4 01601, Ukraine
2Centre de Recherches Mathématiques, Université de Montréal, C.P.6128-Centre Ville, Montréal, QC, Canada H3C 3J7
3Institute of Mathematics, University of Bialystok, Akademicka 2, 15-267 Bialystok, Poland

Received 28 December 2010; Revised 26 May 2011; Accepted 4 June 2011

Academic Editor: N. Govil

Copyright © 2011 Maryna Nesterenko et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recursive algebraic construction of two infinite families of polynomials in variables is proposed as a uniform method applicable to every semisimple Lie group of rank . Its result recognizes Chebyshev polynomials of the first and second kind as the special case of the simple group of type . The obtained not Laurent-type polynomials are equivalent to the partial cases of the Macdonald symmetric polynomials. Recurrence relations are shown for the Lie groups of types , , , , , , and together with lowest polynomials.