English

Integrable Lattice Models for Conjugate $A^{(1)}_n$

High Energy Physics - Theory 2008-11-26 v2 Statistical Mechanics Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Abstract

A new class of An(1)A^{(1)}_n integrable lattice models is presented. These are interaction-round-a-face models based on fundamental nimrep graphs associated with the An(1)A^{(1)}_n conjugate modular invariants, there being a model for each value of the rank and level. The Boltzmann weights are parameterized by elliptic theta functions and satisfy the Yang-Baxter equation for any fixed value of the elliptic nome q. At q=0, the models provide representations of the Hecke algebra and are expected to lead in the continuum limit to coset conformal field theories related to the An(1)A^{(1)}_n conjugate modular invariants.

Keywords

Cite

@article{arxiv.hep-th/0309068,
  title  = {Integrable Lattice Models for Conjugate $A^{(1)}_n$},
  author = {Roger E. Behrend and David E. Evans},
  journal= {arXiv preprint arXiv:hep-th/0309068},
  year   = {2008}
}

Comments

18 pages. v2: minor changes, such as page 11 footnote

R2 v1 2026-07-22T15:18:59.156Z