Orthogonal polynomials of compact simple Lie groups

作     者：Nesterenko, Maryna Patera, Jiří Tereszkiewicz, Agnieszka 

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

出 版 物：《International Journal of Mathematics and Mathematical Sciences》 (Int. J. Math. Math. Sci.)

年 卷 期：2011年第2011卷第unknown期

页      面：1-23页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：ORTHOGONAL polynomials RECURSIVE functions LIE groups LAURENT series WEYL groups 

摘      要：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 A 1. 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 A 1, A 2, A 3, C 2, C 3, G 2, and B 3 together with lowest polynomials. Copyright © 2011 Maryna Nesterenko et al.