%0 Book Section %1 statphys23_0383 %A Deguchi, T. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K algebra chain drinfeld level loop non-crossing onsager polynomial roots rule spin statphys23 symmetry topic-1 unity xxz %T The sl(2) loop algebra symmetry of the XXZ spin chain at roots of unity and the Onsager algebra for the super-integrable chiral Potts model %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=383 %X We present an algorithm by which we can calculate the degenerate multiplicity associated with the sl(2) loop algebra symmetry in the energy spectrum of the XXZ spin chain at roots of unity. We formulate an irreducibility criterion for finite-dimensional highest weight representations of the sl(2) loop algebra. Here we remark that the level crossings at roots of unity in the spectral flow correspond to counterexamples of the level non-crossing rule. We then discuss a novel connection between the Onsager algebra of the superintegrable chiral Potts model and the sl(2) loop algebra. We show that the Drinfeld polynomial of a degenerate eigenspace of some higher-spin XXZ spin chain with respect to the sl(2) loop algebra is equivalent to the polynomial (which we call the SCP polynomial after the Superintegrable Chiral Potts model) introduced by McCoy et al and by Baxter. The SCP polynomial characterizes a corresponding subspace showing the Ising-like spectrum for the superintegrable chiral Potts model (The talk is partially in collaboration with A. Nishino. Ref Phys. Lett. A Vol. 356 (2006) pp. 366-370 (cond-mat/0605551).)

@incollection{statphys23_0383, abstract = {We present an algorithm by which we can calculate the degenerate multiplicity associated with the sl(2) loop algebra symmetry in the energy spectrum of the XXZ spin chain at roots of unity. We formulate an irreducibility criterion for finite-dimensional highest weight representations of the sl(2) loop algebra. Here we remark that the level crossings at roots of unity in the spectral flow correspond to counterexamples of the level non-crossing rule. We then discuss a novel connection between the Onsager algebra of the superintegrable chiral Potts model and the sl(2) loop algebra. We show that the Drinfeld polynomial of a degenerate eigenspace of some higher-spin XXZ spin chain with respect to the sl(2) loop algebra is equivalent to the polynomial (which we call the SCP polynomial after the Superintegrable Chiral Potts model) introduced by McCoy et al and by Baxter. The SCP polynomial characterizes a corresponding subspace showing the Ising-like spectrum for the superintegrable chiral Potts model (The talk is partially in collaboration with A. Nishino. [Ref] Phys. Lett. A Vol. 356 (2006) pp. 366-370 (cond-mat/0605551).)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Deguchi, T.}, biburl = {https://www.bibsonomy.org/bibtex/29077d0c8e0b9d3413a075e42819c5cf5/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {6d6babd854dfd1ecb2d8ee9fa0f68524}, intrahash = {9077d0c8e0b9d3413a075e42819c5cf5}, keywords = {algebra chain drinfeld level loop non-crossing onsager polynomial roots rule spin statphys23 symmetry topic-1 unity xxz}, month = {9-13 July}, timestamp = {2007-06-20T10:16:18.000+0200}, title = {The sl(2) loop algebra symmetry of the XXZ spin chain at roots of unity and the Onsager algebra for the super-integrable chiral Potts model}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=383}, year = 2007 }