On the Degenerate Multiplicity of the Loop Algebra for the 6V Transfer Matrix at Roots of Unity
arXiv:cond-mat/0602427 · doi:10.3842/SIGMA.2006.021
Abstract
We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the loop algebra symmetry if the parameter is given by a root of unity, , for an integer . We discuss the dimensions of the degenerate eigenspace generated by a regular Bethe state in some sectors, rigorously as follows: We show that every regular Bethe ansatz eigenvector in the sectors is a highest weight vector and derive the highest weight , which leads to evaluation parameters . If the evaluation parameters are distinct, we obtain the dimensions of the highest weight representation generated by the regular Bethe state.
arXiv commentPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
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