Paths for Z_k parafermionic models

Abstract

We present a simple bijection between restricted (Bressoud) lattice paths and RSOS paths in regime II. Both types of paths describe states in Z_k parafermionic irreducible modules. The bijection implies a direct correspondence between a RSOS path and a parafermionic state in a quasi-particle basis.

17 pages- minor corrections plus a concluding remark

References in corpus (7)

• Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
• Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
• Combinatorial constructions of modules for infinite-dimensional Lie algebras, II. Parafermionic space
• Parafermionic quasi-particle basis and fermionic-type characters
• Parafermionic character formulae
• Parafermionic derivation of Andrews-type multiple sums
• Multiple partitions, lattice paths and a Burge-Bressoud-type correspondence

Cited by in corpus (4)

• New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions
• A bijection between paths for the M(p,2p+1) minimal model Virasoro characters
• Paths and partitions: combinatorial descriptions of the parafermionic states
• Nonlocal operator basis from the path representation of the M(k+1,k+2) and the M(k+1,2k+3) minimal models