Orthogonal Polynomials of Compact Simple Lie Groups

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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Main Authors: Maryna Nesterenko, Jiří Patera, Agnieszka Tereszkiewicz
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2011/969424
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spelling doaj-a55e29716af9479391013ff39dde92d22020-11-24T23:28:06ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/969424969424Orthogonal Polynomials of Compact Simple Lie GroupsMaryna Nesterenko0Jiří Patera1Agnieszka Tereszkiewicz2Department of Applied Research, Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Street, Kyiv-4 01601, UkraineCentre de Recherches Mathématiques, Université de Montréal, C.P.6128-Centre Ville, Montréal, QC, H3C 3J7, CanadaInstitute of Mathematics, University of Bialystok, Akademicka 2, 15-267 Bialystok, PolandRecursive 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.http://dx.doi.org/10.1155/2011/969424
collection DOAJ
language English
format Article
sources DOAJ
author Maryna Nesterenko
Jiří Patera
Agnieszka Tereszkiewicz
spellingShingle Maryna Nesterenko
Jiří Patera
Agnieszka Tereszkiewicz
Orthogonal Polynomials of Compact Simple Lie Groups
International Journal of Mathematics and Mathematical Sciences
author_facet Maryna Nesterenko
Jiří Patera
Agnieszka Tereszkiewicz
author_sort Maryna Nesterenko
title Orthogonal Polynomials of Compact Simple Lie Groups
title_short Orthogonal Polynomials of Compact Simple Lie Groups
title_full Orthogonal Polynomials of Compact Simple Lie Groups
title_fullStr Orthogonal Polynomials of Compact Simple Lie Groups
title_full_unstemmed Orthogonal Polynomials of Compact Simple Lie Groups
title_sort orthogonal polynomials of compact simple lie groups
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2011-01-01
description 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.
url http://dx.doi.org/10.1155/2011/969424
work_keys_str_mv AT marynanesterenko orthogonalpolynomialsofcompactsimpleliegroups
AT jiripatera orthogonalpolynomialsofcompactsimpleliegroups
AT agnieszkatereszkiewicz orthogonalpolynomialsofcompactsimpleliegroups
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