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**1 - 6**of**6**### HIGHER SPIN POLYNOMIAL SOLUTIONS OF QUANTUM KNIZHNIK–ZAMOLODCHIKOV EQUATION

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### Bethe ansatz solvability and supersymmetry of the M2 model of single fermions

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### The nineteen-vertex model and alternating sign matrices

, 2014

"... It is shown that the transfer matrix of the inhomogeneous nineteen-vertex model with certain diagonal twisted boundary conditions possesses a simple eigenvalue. This is achieved through the identification of a simple and completely explicit solution of its Bethe equations. The corresponding eigenvec ..."

Abstract
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It is shown that the transfer matrix of the inhomogeneous nineteen-vertex model with certain diagonal twisted boundary conditions possesses a simple eigenvalue. This is achieved through the identification of a simple and completely explicit solution of its Bethe equations. The corresponding eigenvector is computed by means of the algebraic Bethe ansatz, and its square norm is shown to be related to the Izergin-Korepin determinant. In the homogeneous limit, the vector coincides with the supersymmetry singlet of the twisted spin−1 XXZ chain. It is proven that in a natural polynomial normalisation scheme its square norm coincides with a generating function for weighted enumeration of alternating sign matrices.