Smirnov-type integral formulae for correlation functions of the bulk/boundary XXZ model in the anti-ferromagnetic regime

Presented are the integral solutions to the quantum Knizhnik-Zamolodchikov equations for the correlation functions of both the bulk and boundary XXZ models in the anti-ferromagnetic regime. The difference equations can be derived from Smirnov-type master equations for correlation functions on the basis of the CTM bootstrap. Our integral solutions with an appropriate choice of the integral kernel reproduce the formulae previously obtained by using the bosonization of the vertex operators of the quantum affine algebra $U_q (\hat{\mathfrak{sl}_2})$.Comment: 21pages, LaTex2

Quantum Knizhnik-Zamolodchikov equations of level 0 and form factors in SOS model

The cyclic SOS model is considered on the basis of Smirnov's form factor bootstrap approach. Integral solutions to the quantum Knizhnik-Zamolodchikov equations of level 0 are presented.Comment: 11pages, LaTex2

Polynomial identities of the Rogers--Ramanujan type

Presented are polynomial identities which imply generalizations of Euler and Rogers--Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical one-to-one correspondence between those two kinds of restricted partitions.Comment: 27 page

Virasoro character identities from the Andrews--Bailey construction

We prove $q$-series identities between bosonic and fermionic representations of certain Virasoro characters. These identities include some of the conjectures made by the Stony Brook group as special cases. Our method is a direct application of Andrews' extensions of Bailey's lemma to recently obtained polynomial identities.Comment: 22 pages. Expanded version with new result

A Vertex Operator Approach for Form Factors of Belavin's (Z/nZ)(\mathbb{Z}/n\mathbb{Z})-Symmetric Model and Its Application

A vertex operator approach for form factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is constructed on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. As simple application for $n=2$, we obtain expressions for $2m$-point form factors related to the $\sigma^z$ and $\sigma^x$ operators in the eight-vertex model.Comment: partly based on a talk given in International Workshop RAQIS'10, Recent Advances in Quantum Integrable Systems, held at LAPTH, Annecy-le-Vieux, France, 15--18 June 201

Spontaneous Polarization of the Zn\Bbb Z _{n}-Baxter Model

We show that correlation functions of the \bz _n -Baxter model in the principal regime satisfy a system of difference equations. We obtain the spontaneous polarization of the \bz _n -Baxter model as a solution of the simplest difference equation.Comment: 14p, RIMS-93