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Quantum Knizhnik-Zamolodchikov equation for \(U_ q(\widehat{\mathfrak sl}_ n)\) and integral formula. (English) Zbl 0844.17011

Summary: An integral formula for solutions to the level-zero quantum Knizhnik-Zamolodchikov equation associated with the vector representation of \(U_q (\widehat {{\mathfrak sl}_n})\) is presented. This formula gives a generalization of both our previous work for \(U_q (\widehat {{\mathfrak sl}_2})\) [M. Jimbo, T. Kojima, T. Miwa and Y.-H. Quano, ibid. 27, 3267-3283 (1994; Zbl 0842.17030)] and Smirnov’s formula for form factors of the \(SU (n)\) chiral Gross-Neveu model [F. A. Smirnov, Form factors in completely integrable models of quantum field theory, World Scientific Singapore (1992; Zbl 0788.46077)].

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
39B52 Functional equations for functions with more general domains and/or ranges
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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