A new (in)finite dimensional algebra for quantum integrable models
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 ``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.
Cite
@article{arxiv.math-ph/0503036,
title = {A new (in)finite dimensional algebra for quantum integrable models},
author = {P. Baseilhac and K. Koizumi},
journal= {arXiv preprint arXiv:math-ph/0503036},
year = {2014}
}
Comments
17 pages; LaTeX file with amssymb; v2: typos corrected, references added, minor changes;v3: other typos corrected, version to appear in Nucl.Phys.B