Letters in Mathematical Physics

, Volume 81, Issue 3, pp 211–226 | Cite as

Paths for \({\mathcal{Z}}_k\) Parafermionic Models

  • Patrick Jacob
  • Pierre Mathieu


We present a simple bijection between restricted Bressoud lattice paths and paths in regime II of the Andrews–Baxter–Forrester restricted solid–on–solid model. Both types of paths describe states in \({\mathcal{Z}}_k\) parafermionic irreducible modules. The bijection implies a direct correspondence between a RSOS path and a parafermionic state in a quasi-particle basis.

Mathematics Subject Classifications (2000)

81T40 82B23 82B20 11P21 05A17 05A19 


lattice paths RSOS models parafermions quasi-particles fermionic characters 


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© Springer 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of DurhamDurhamUK
  2. 2.Département de physique, de génie physique et d’optiqueUniversité LavalQuébecCanada

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