On the Degenerate Multiplicity of the $s{l}_2$ Loop Algebra for the 6V Transfer Matrix at Roots of Unity

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 $s{l}_2$ loop algebra symmetry if the $q$ parameter is given by a root of unity, $q_0^{2N}=1$, for an integer $N$. 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 ${\bar{d}}_k^{\pm }$, which leads to evaluation parameters $a_j$. If the evaluation parameters are distinct, we obtain the dimensions of the highest weight representation generated by the regular Bethe state.

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (3)

• New Developments in the Eight Vertex Model
• The six-vertex model at roots of unity and some highest weight representations of the sl(2) loop algebra
• XXZ Bethe states as highest weight vectors of the $s{l}_2$ loop algebra at roots of unity

Cited by in corpus (1)

• Popcorn Drude weights from quantum symmetry