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Abstract

Abstract. The Wakimoto construction for the quantum affine algebra U q ( sl 2 ) admits a reduction to the q-deformed parafermion algebras. We interpret the latter theory as a free field realization of the Andrews-Baxter-Forrester models in regime II. We give multi-particle form factors of some local operators on the lattice and compute their scaling limit, where the models are described by a massive field theory with Z k symmetric minimal scattering matrices.math.QA/0001071

On scaling fields in Z N Ising models

“…We follow the algebraic approach [11,12,14,17] to the form factors originated from the analysis of lattice ABF model [15]. This lattice model falls into the same universality class as the Z N Ising model.…”

Free field construction for the eight-vertex model: representation for form factors

“…The symmetry of the eight-vertex model was conjectured to be the elliptic algebra A q,p ( sl 2 ) [5], but neither low-temperature expansion check was performed nor bosonization of this algebra was acheived. The only encouraging result is its relation to the elliptic algebra E τ,η ( sl 2 ) describing the SOS model [18,19]. One might expect a natural solution of the problem of m and u 0 independence in this framework.…”

Quasi-Hopf superalgebras and elliptic quantum supergroups

“…The proof of ͑IV.5͒ is identical to the nonsuper case given by Jimbo et al, 4 apart from the use of the graded tensor products. Moreover, it is easily seen that F() obeys the counit property…”

“…Following Jimbo et al, 4 we say this twistor is of vertex type. Let us write h i ϭ␣ i (iϭ0,1,...,2nϪ1) with ␣ i given by ͑IV.26͒.…”

“…Our interest in quasi-Hopf algebras was ignited by Bo-Yu Hou's beautiful lecture on the Jimbo et al paper 4 when YZZ was visiting Northwest University, Xi'an, in December 1997. YZZ thanks Bo-Yu Hou for interesting him in the subject and for helpful discussions.…”