On the Degenerate Multiplicity of the $sl_2$ Loop Algebra for the 6V Transfer Matrix at Roots of Unity
| dc.creator | Deguchi, Tetsuo | |
| dc.date | 2006-02-17 | |
| dc.date.accessioned | 2026-07-07T09:34:20Z | |
| dc.date.available | 2026-07-07T09:34:20Z | |
| dc.description | 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 $sl_2$ 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. | |
| dc.description | Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0602427 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0602427 | |
| dc.identifier | SIGMA 2 (2006), 021, 10 pages | |
| dc.identifier | doi:10.3842/SIGMA.2006.021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159455 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mathematical Physics | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | On the Degenerate Multiplicity of the $sl_2$ Loop Algebra for the 6V Transfer Matrix at Roots of Unity | |
| dc.type | text |