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

  • I. Quantum Groups, Deformation Theory And Representation Theory
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Quantum Groups

Part of the book series: Lecture Notes in Mathematics ((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.

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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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Petr P. Kulish

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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

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