English

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

Mathematical Physics 2014-11-18 v3 Statistical Mechanics High Energy Physics - Theory math.MP Quantum Algebra Exactly Solvable and Integrable Systems

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 ``qq-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.

Keywords

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