2005/03/31 by Pascal Baseilhac, P. Baseilhac, Kozo Koizumi +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Integrable system #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #cond-mat.stat-mech #hep-th #math-ph #math.MP #math.QA #nlin.SI
paper · pdf · doi:10.1016/j.nuclphysb.2005.05.021
published as Nucl.Phys.B720:325-347,2005 · 17 pages; LaTeX file with amssymb; v2: typos corrected, references added, minor changes;v3: other typos corrected, version to appear in Nucl.Phys.B
arxiv created 2005/06/01 · openalex publication_date 2005/06/20 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.