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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| 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. |
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| ISSN: | 0161-1712 1687-0425 |