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Some integral formulas for the solutions of the \(\text{sl}_2\) dKZ equation with level \({-4}\). (English) Zbl 0985.82504

Summary: A direct proof is given of the fact that the integral formula for the \(XXX\) limit of the trace of the type I \(q\)-vertex operators satisfies the deformed Knizhnik-Zamolodchikov (dKZ) equation with level \(-4\). We also carry out one-time integration by taking the residue at infinity. As a corollary we can construct a family of the integral formulas for solutions to the dKZ equation. Another corollary is the integral formula for the correlation function of the inhomogeneous \(XXX\) model, whose number of integrals is less than that of the previously obtained correlator for the \(XXZ\) model.

MSC:

82B23 Exactly solvable models; Bethe ansatz
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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