Root of unity symmetries in the 8 and 6 vertex models

Abstract

We review the recently discovered symmetries of the 8 and 6 vertex models which exist at roots of unity and present their relation with representation theory of affine Lie algebras, Drinfeld polynomials and Bethe vectors.

arXiv comment13 pages, to appear in Proceedings of the RIMS 2004 workshop on "Recent Progress in Solvable Lattice Models"

References in corpus (6)

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• The Importance of being Odd
• Cyclic monodromy matrices for sl(n) trigonometric R-matrices
• The XXZ spin chain at $\Delta =-1/2$: Bethe roots, symmetric functions and determinants
• Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
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Cited by in corpus (6)

• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• Fusion Operators in the Generalized ${\tau }^{(2)}$-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
• The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity $\eta =\frac{2mK}{N}$ for odd N
• The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of $U_q(s{l}_2)$
• On $Q$-operators of XXZ Spin Chain of Higher Spin
• Representation Theory and Baxter's TQ equation for the six-vertex model. A pedagogical overview