The Highest Weight Property for the $S{U}_q(n)$ Invariant Spin Chains

Abstract

The $S{U}_q(n)$ generators are obtained as large spectral parameter limit of the Yang-Baxter operators in the integrable $S{U}_q(n)$ invariant vertex model. The commutation relations, including Serre relations, are obtained as limits of the Yang-Baxter equations. The recently found eigenvectors of the $S{U}_q(n)$ invariant spin chains are shown to be Highest Weight vectors of the corresponding quantum group.

9 pages, Latex, LPTHE-PAR 94/13. (Two references added)

References in corpus (4)

• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case
• Bethe Ansatz and Quantum Groups: The Light--Cone Approach. II. From RSOS($p+1$) models to $p-$restricted Sine--Gordon Field Theories
• Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance

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