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 sl2 loop
algebra symmetry if the q parameter is given by a root of unity,
q02N=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 dˉk±, which
leads to evaluation parameters aj. If the evaluation parameters are
distinct, we obtain the dimensions of the highest weight representation
generated by the regular Bethe state.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA