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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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/969424 |
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| author | Maryna Nesterenko Jiří Patera Agnieszka Tereszkiewicz |
| author_facet | Maryna Nesterenko Jiří Patera Agnieszka Tereszkiewicz |
| author_sort | Maryna Nesterenko |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-a55e29716af9479391013ff39dde92d2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a55e29716af9479391013ff39dde92d22025-02-03T06:42:28ZengWileyInternational 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 |
| spellingShingle | Maryna Nesterenko Jiří Patera Agnieszka Tereszkiewicz Orthogonal Polynomials of Compact Simple Lie Groups International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Orthogonal Polynomials of Compact Simple Lie Groups |
| title_sort | orthogonal polynomials of compact simple lie groups |
| url | http://dx.doi.org/10.1155/2011/969424 |
| work_keys_str_mv | AT marynanesterenko orthogonalpolynomialsofcompactsimpleliegroups AT jiripatera orthogonalpolynomialsofcompactsimpleliegroups AT agnieszkatereszkiewicz orthogonalpolynomialsofcompactsimpleliegroups |