Quantum Groups pp 142-147 | Cite as

Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials

  • Kimio Ueno
  • Tadayoshi Takebayashi
I. Quantum Groups, Deformation Theory And Representation Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1510)


We will study zonal spherical functions on quantum symmetric space GL q (N+1)/O q (N+1)), and will show that those for the case N=2 are given by Macdonald's polynomials of the A2 type. Some q-analogues of hypergeometric series associated with the quantum symmetric spaces will be discussed.

Key words and phrases

Zonal spherical functions quantum symmetric spaces Macdonald's symmetric polynomials 


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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Kimio Ueno
    • 1
  • Tadayoshi Takebayashi
    • 1
  1. 1.Department of MathematicsWaseda UniversityTokyoJapan

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