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

P. Baseilhac·K. Koizumi
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Abstract

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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BibTeXRIS

P. Baseilhac, K. Koizumi. 2005-03-14. A new (in)finite dimensional algebra for quantum integrable models. https://doi.org/10.1016/j.nuclphysb.2005.05.021

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