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Orthogonal Polynomials of Compact Simple Lie Groups

Author

Listed:
  • Maryna Nesterenko
  • Jiří Patera
  • Agnieszka Tereszkiewicz

Abstract

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

Suggested Citation

  • Maryna Nesterenko & Jiří Patera & Agnieszka Tereszkiewicz, 2011. "Orthogonal Polynomials of Compact Simple Lie Groups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-23, November.
    • Handle: RePEc:hin:jijmms:969424
    DOI: 10.1155/2011/969424
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