Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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   We identify the quantum group ${\Large\textsl{U}}_\textsl{w}(sl_2)$ 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
${\Large\textsl{U}}_\omega(sl_2)$-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.

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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph