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

I. Quantum Groups, Deformation Theory And Representation Theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 1510)

Abstract

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 A 2 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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References

  1. Jimbo, M., A q-analogue of U q(gl(N + 1)), Hecke algebra, and the Yang-Baxter equation, Lett. Math.Phys. 11 (1986), 247.

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© 1992 Springer-Verlag

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Ueno, K., Takebayashi, T. (1992). Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials. In: Kulish, P.P. (eds) Quantum Groups. Lecture Notes in Mathematics, vol 1510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101186

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  • DOI: https://doi.org/10.1007/BFb0101186

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55305-2

  • Online ISBN: 978-3-540-47020-5

  • eBook Packages: Springer Book Archive