The Spectral Problem for the q-Knizhnik-Zamolodchikov Equation

Abstract

We analyse the spectral problem for the q-Knizhnik-Zamolodchikov equations for $U_q(\widehat{s{l}_2})(0<q\le 1)$ at level zero. The case of 2-point functions in the fundamental representation is studied in detail. The scattering states are found explicitly in terms of continuous q-Jacobi polynomials. The corresponding S-matrix is shown to coincide, up to a trivial factor, with the kink-antikink S-matrix in the spin-1/2 XXZ antiferromagnet.

11 pages

References in corpus (4)

• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the $p$-Adics-Quantum Group Connection
• Excitation Scattering in Integrable Models and Hall-Littlewood-Kerov Polynomials
• $Z_n$ Baxter Models and Quantum Symmetric Spaces

Cited by in corpus (2)

• 5D partition functions, q-Virasoro systems and integrable spin-chains
• The Spectral Problem for the q-Knizhnik-Zamolodchikov Equation and Continuous q-Jacobi Polynomials