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| HAL: hal-00019440, version 1 |
| arXiv: math-ph/0503036 |
| Detailed view |  Export this paper |
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| Nuclear Physics B 720 (2005) 325-347 |
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| A new (in)finite dimensional algebra for quantum integrable models |
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| P. Baseilhac 1K. Koizumi 1 |
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| (2005) |
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| 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. |
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| 1: | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| Subject | : | Mathematics/Mathematical Physics Physics/Mathematical Physics Mathematics/Quantum Algebra Nonlinear Sciences/Exactly Solvable and Integrable Systems Physics/Condensed Matter/Statistical Mechanics Physics/High Energy Physics - Theory |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/math-ph/0503036 |
| hal-00019440, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00019440 | |
| oai:hal.archives-ouvertes.fr:hal-00019440 | |
| From: Import arXiv | |
| Submitted on: Tuesday, 21 February 2006 20:37:12 | |
| Updated on: Tuesday, 21 February 2006 20:37:12 | |
