Abstract.A new approach to the correlation functions is presented for the XXZ model in the anti-ferroelectric regime. The method is based on the recent realization of the quantum affine symmetry using vertex operators. With the aid of a boson representation for the latter, an integral formula is found for correlation functions of arbitrary local operators. As a special case it reproduces the spontaneous staggered polarization obtained earlier by Baxter.
A (q,γ) analog of the W1+∞ algebra is introduced. Irreducible quasifinite highest weight modules of this algebra and R matrices acting on a tensor product of these modules are investigated. A connection with the q deformed Virasoro and WN algebras is also discussed.
We formulate the basic properties of q-vertex operators in the context of the Andrews-Baxter-Forrester (ABF) series, as an example of face-interaction models, derive the q-difference equations satisfied by their correlation functions, and establish their connection with representation theory. We also discuss the q-difference equations of the Kashiwara-Miwa (KM) series, as an example of edge-interaction models.Next, the Ising model-the simplest special case of both ABF and KM series-is studied in more detail using the Jordan-Wigner fermions. In particular, all matrix elements of vertex operators are calculated.
The representation theory of the SO(3) invariant superconformal algebra is discussed. The necessary and sufficient condition of unitarity, the Kac determinants, the character formulae for unitary representations and their modular transformation laws are obtained under some assumptions.
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