Lattice models and generalized Rogers Ramanujan identities

Abstract

We revisit the solvable lattice models described by Andrews Baxter and Forrester and their generalizations. The expressions for the local state probabilities were shown to be related to characters of the minimal models. We recompute these local state probabilities by a different method. This yields generalized Rogers Ramanujan identities, some of which recently conjectured by Kedem et al. Our method provides a proof for some cases, as well as generating new such identities.

References in corpus (5)

• Fermionic Sum Representations for Conformal Field Theory Characters
• Fermionic Quasi-Particle Representations for Characters of $(G^{(1)}{)}_1\times (G^{(1)}{)}_1ø(G^{(1)}{)}_2$
• Dilogarithm Identities in Conformal Field Theory
• Fermionic Character Sums and the Corner Transfer Matrix
• Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz

Cited by in corpus (7)

• Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
• Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4ν)
• Multinomials and Polynomial Bosonic Forms for the Branching Functions of the $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$ Conformal Coset Models
• Level Two String Functions and Rogers Ramanujan Type Identities
• On The Characters of Parafermionic Field Theories
• Generalized Rogers Ramanujan Identities for Twisted Affine Algebras
• The $\mathbf{SO}(2\mathbf{r}{)}_2$ string functions as $\mathbf{q}$-diagrams