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- W1762579084 abstract "We identify the quantum group ${Largetextsl{U}}_textsl{w}(sl_2)$ in the $L$-operator of $tau^{(2)}$-model for a generic $textsl{w}$ as a subalgebra of $U_{sf q} (sl_2)$ with $textsl{w} = {sf q}^{-2}$. In the roots of unity case, ${sf q}=q, textsl{w} = omega$ with $q^{{bf n}} = omega^N = 1$, the eigenvalues and eigenvectors of XXZ-model with the $U_q (sl_2)$-cyclic representation are determined by the $tau^{(2)}$-model with the induced ${Largetextsl{U}}_omega(sl_2)$-cyclic representation, which is decomposed as a finite sum of $tau^{(2)}$-models in non-superintegrable inhomogeneous $N$-state chiral Potts model. Through the theory of chiral Potts model, the $Q$-operator of XXZ-model can be identified with the related chiral Potts transfer matrices, with special features appeared in the ${bf n}=2N$, e.g. $N$ even, case. We also establish the duality of $tau^{(2)}$-models related to cyclic representations of $U_q (sl_2)$, analogous to the $tau^{(2)}$-duality in chiral Potts model; and identify the model dual to the XXZ model with $U_q (sl_2)$-cyclic representation." @default.
- W1762579084 created "2016-06-24" @default.
- W1762579084 creator A5037516673 @default.
- W1762579084 date "2012-06-19" @default.
- W1762579084 modified "2023-09-27" @default.
- W1762579084 title "Quantum Group Theory in $tau^{(2)}$-model, Duality of $tau^{(2)}$-model and XXZ-model with Cyclic ${bf U_q(sl_2)}$-representation for ${bf q^n =1}$, and Chiral Potts Model" @default.
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