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SIGMA 2 (2006), 021, 10 pages cond-mat/0602427
https://doi.org/10.3842/SIGMA.2006.021
On the Degenerate Multiplicity of the sl2 Loop Algebra for the 6V Transfer Matrix at Roots of Unity
Tetsuo Deguchi
Department of Physics, Faculty of Science, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-Ku, Tokyo 112-8610, Japan
Received October 31, 2005, in final form February 06, 2006; Published online February 17, 2006
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 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
dk±,
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.
Key words:
loop algebra; the six-vertex model; roots of unity representations of quantum groups; Drinfeld polynomial.
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