A new (in)finite dimensional algebra for quantum integrable models
Baseilhac, P. ; Koizumi, K.
arXiv, 0503036 / Harvested from arXiv
Text on arXiv
A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and mutually commuting quantities - which ensure the integrability of the system - are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan-Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite dimensional algebra is a ``$q-$deformed'' analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models.
Publié le : 2005-03-14
Classification:  Mathematical Physics,  Condensed Matter - Statistical Mechanics,  High Energy Physics - Theory,  Mathematics - Quantum Algebra,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0503036,
     author = {Baseilhac, P. and Koizumi, K.},
     title = {A new (in)finite dimensional algebra for quantum integrable models},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0503036}
}

Baseilhac, P.; Koizumi, K. A new (in)finite dimensional algebra for quantum integrable models. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0503036/