The spectral problem for the q-Knizhnik-Zamolodchikov equation and continuous q-Jacobi polynomials

Peter G.O. Freund, Anton V. Zabrodin

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22 Citations (Scopus)

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 languageEnglish
Pages (from-to)17-42
Number of pages26
JournalCommunications in Mathematical Physics
Volume173
Issue number1
DOIs
Publication statusPublished - Oct 1995
Externally publishedYes

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