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 ℓ. 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 ℓ/2 XXZ) or loop models in the root of unity case \({q=-e^{-i\pi/(\ell+2)}}\) .
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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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DOI: https://doi.org/10.1007/s00220-014-1963-7