## Abstract

The spectral problem for the q-Knizhnik-Zamolodchikov equations for {Mathematical expression} at arbitrary non-negative level k 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 continuous q-Jacobi polynomials, and the S-matrix is derived from their asymptotic behavior. The level zero S-matrix is closely connected with the kink-antikink S-matrix for the spin- {Mathematical expression} 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 on p-adic groups with the prime p given by p=q^{-2}.

Original language | English |
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Pages (from-to) | 17-42 |

Number of pages | 26 |

Journal | Communications in Mathematical Physics |

Volume | 173 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 1995 |

Externally published | Yes |