Orthogonal Polynomials of Compact Simple Lie Groups

Recursive algebraic construction of two infinite families of polynomials in n variables is proposed as a uniform method applicable to every semisimple Lie group of rank n. Its result recognizes Chebyshev polynomials of the first and second kind as the special case of the simple group of type A1. The...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences 2011, Vol.2011 (2011), p.680-702-145
Main Authors: Nesterenko, Maryna, Patera, Jiří, Tereszkiewicz, Agnieszka
Format: Article
Language:English
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Summary:Recursive algebraic construction of two infinite families of polynomials in n variables is proposed as a uniform method applicable to every semisimple Lie group of rank n. Its result recognizes Chebyshev polynomials of the first and second kind as the special case of the simple group of type A1. 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 A1, A2, A3, C2, C3, G2, and B3 together with lowest polynomials.
ISSN:0161-1712
1687-0425
DOI:10.1155/2011/969424