# Root of unity symmetries in the 8 and 6 vertex models

@article{Fabricius2004RootOU, title={Root of unity symmetries in the 8 and 6 vertex models}, author={Klaus Fabricius and Barry M McCoy}, journal={arXiv: Statistical Mechanics}, year={2004} }

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.

## 12 Citations

### Representation theory and Baxter's TQ equation for the six-vertex model. A pedagogical overview.

- Mathematics
- 2004

A summary of the construction procedure of generalized versions of Baxter's Q-operator is given. Illustrated by several figures and diagrams the use of representation theory is explained step-by-step…

### Representation Theory and Baxter's TQ equation for the six-vertex model. A pedagogical overview.(Solvable Lattice Models 2004 : Recent Progress on Solvable Lattice Models )

- Mathematics
- 2006

Recent years have seen renewed interest in the six and eight-vertex model at rational coupling values, that is when the crossing parameter is evaluated at roots of unity. Deguchi, Fabricius and McCoy…

### The Q-operator for root-of-unity symmetry in the six-vertex model

- Mathematics
- 2006

We construct the explicit Q-operator incorporated with the sl2-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the Q-operator, the six-vertex…

### Se p 20 06 Fusion Operators in the Generalized τ ( 2 )-model and the Root-of-unity Symmetry of Six-vertex Model with Arbitrary Spin

- Mathematics
- 2006

We construct the fusion operators in the generalized τ (2)-model using the fused L-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe Ansatz discussion is…

### Fusion operators in the generalized τ(2)-model and root-of-unity symmetry of the XXZ spin chain of higher spin

- Mathematics
- 2007

We construct the fusion operators in the generalized τ(2)-model using the fused L-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe-ansatz discussion is…

### The Q-operator and functional relations of the eight-vertex model at root-of-unity for odd N

- Mathematics
- 2006

Following Baxter's method of producing Q72-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the crossing parameter with odd N where Q72 does not exist. We use this…

### A Q-operator for the twisted XXX model

- Mathematics
- 2006

Taking the isotropic limit Δ → 1 in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX…

### N ov 2 00 6 The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity η = 2 mK N for odd N

- Mathematics
- 2006

Following Baxter's method of producing Q 72-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the parameter η = 2mK N with odd N where Q 72 does not exist. We use this…

### Ja n 20 07 Fusion Operators in the Generalized τ ( 2 )-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin 1

- Mathematics
- 2007

We construct the fusion operators in the generalized τ (2)-model using the fused L-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe ansatz discussion is…

### The transfer matrix of a superintegrable chiral Potts model as the Q operator of root-of-unity XXZ chain with cyclic representation of

- Mathematics
- 2007

We demonstrate that the transfer matrix of the inhomogeneous N-state chiral Potts model with two vertical superintegrable rapidities serves as the Q operator of the XXZ chain model for a cyclic…

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