Higher spin polynomial solutions of quantum Knizhnik--Zamolodchikov equation

Abstract

We provide explicit formulae for highest-weight to highest-weight correlation functions of perfect vertex operators of $U_q(\widehat{\mathfrak{sl}(2)})$ at arbitrary integer level $\ell$. 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 $\ell /2$ XXZ) or loop models in the root of unity case $q=-e^{-i\pi /(\ell +2)}$.

References in corpus (4)

• Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
• Generalization of the matrix product ansatz for integrable chains
• Combinatorial point for higher spin loop models
• Subrepresentations in the Polynomial Representation of the Double Affine Hecke Algebra of type $G{L}_n$ at $t^{k+1}{q}^{r-1}=1$

Cited by in corpus (1)

• Symmetry classes of alternating sign matrices in the nineteen-vertex model