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Higher Spin Polynomial Solutions of Quantum Knizhnik–Zamolodchikov Equation

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Abstract

We provide explicit formulae for highest-weight to highest-weight correlation functions of perfect vertex operators of \({U_q(\widehat{\mathfrak{sl}(2)})}\) in arbitrary integer level . They are given in terms of certain Macdonald polynomials. We apply this construction to the computation of the ground state of higher spin vertex models, spin chains (spin /2 XXZ) or loop models in the root of unity case \({q=-e^{-i\pi/(\ell+2)}}\) .

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Correspondence to Paul Zinn-Justin.

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Communicated by N. Reshetikhin

TF was based at the Centre de Recherches Mathématiques at UdeM while most of the work was carried out. He is currently supported by ANR-10-BLAN-0120-03 “DIADEMS”. Preprint LAPTh-060/12.

PZJ is supported in part by ERC grant 278124 “LIC”. He would like to thank N. Reshetikhin and R. Weston for discussions.

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Fonseca, T., Zinn-Justin, P. Higher Spin Polynomial Solutions of Quantum Knizhnik–Zamolodchikov Equation. Commun. Math. Phys. 328, 1079–1115 (2014). https://doi.org/10.1007/s00220-014-1963-7

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