Abstract
The spectral problem for theq-Knizhnik-Zamolodchikov equations for\(Uq(\widehat{sl_2 })(0< q< 1)\) at arbitrary non-negative levelk is considered. The case of two-point functions in the fundamental representation is studied in detail. The scattering states are given explicitly in terms of continuousq-Jacobi polynomials, and theS-matrix is derived from their asymptotic behavior. The level zeroS-matrix is closely connected with the kink-antikinkS-matrix for the spin-\(\tfrac{1}{2}\) XXZ antiferromagnet. An interpretation of the latter in terms of scattering on (quantum) symmetric spaces is discussed. In the limit of infinite level we observe connections with harmonic analysis onp-adic groups with the primep given byp=q −2.
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Communicated by G. Felder
Work supported in part by the NSF: PHY-91-23780
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Freund, P.G.O., Zabrodin, A.V. The spectral problem for theq-Knizhnik-Zamolodchikov equation and continuousq-Jacobi polynomials. Commun.Math. Phys. 173, 17–42 (1995). https://doi.org/10.1007/BF02100180
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DOI: https://doi.org/10.1007/BF02100180