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The twisted XXZ chain at roots of unity revisited

Christian Korff
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Abstract

The symmetries of the twisted XXZ spin-chain (alias the twisted six-vertex model) at roots of unity are investigated. It is shown that when the twist parameter is chosen to depend on the total spin an infinite-dimensional non-abelian symmetry algebra can be explicitly constructed for all spin sectors. This symmetry algebra is identified to be the upper or lower Borel subalgebra of the sl_2 loop algebra. The proof uses only the intertwining property of the six-vertex monodromy matrix and the familiar relations of the six-vertex Yang-Baxter algebra.

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Christian Korff. 2003-08-22. The twisted XXZ chain at roots of unity revisited. https://doi.org/10.1088/0305-4470%2F37%2F5%2F014

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