A new (in)finite dimensional algebra for quantum integrable models

Details A new (in)finite dimensional algebra for quantum integrable models A new (in)finite dimensional algebra for quantum integrable models

2005-03-14

arxiv.org/abs/math-ph/0503036v3

Nucl.Phys. B720 (2005) 325-347

Physics

Mathematical Physics

17 pages; LaTeX file with amssymb; v2: typos corrected, references added, minor changes;v3: other typos corrected, version to

Scientific paper

10.1016/j.nuclphysb.2005.05.021

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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