The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra

After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a fusion of the vertex operators of U_{q,p}(sl_N^). The basic generating functions \Lambda_j(z) (j=1,2,.. N-1) of the deformed W_N algebra are derived explicitly.Comment: 15 pages, to appear in Journal of physics A special issue - RAQIS0

Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model

Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model and tail operators are expressed in terms of bosonized vertex operators in the $A^{(1)}_{n-1}$ model. Correlation functions of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model can be obtained by using these objects, in principle. In particular, we calculate spontaneous polarization, which reproduces the result by myselves in 1993.Comment: For the next thirty days the full text of this article is available at http://stacks.iop.org/1751-8121/42/16521

Bilinear structure and Schlesinger transforms of the qq-PIII_{\rm III} and qq-PVI_{\rm VI} equations

We show that the recently derived ($q$-) discrete form of the Painlev\'e VI equation can be related to the discrete P$_{\rm III}$, in particular if one uses the full freedom in the implementation of the singularity confinement criterion. This observation is used here in order to derive the bilinear forms and the Schlesinger transformations of both $q$-P$_{\rm III}$ and $q$-P$_{\rm VI}$.Comment: 10 pages, Plain Te

Algebraic representation of correlation functions in integrable spin chains

Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the physically interesting homogeneous chains. We discuss also the case of quantum group invariant operators and generalization to the XYZ chain.Comment: 31 pages, no figur

Elliptic Deformed Superalgebra uq,p(sl^(M∣N))u_{q,p}(\hat{{sl}}(M|N))

We introduce the elliptic superalgebra $U_{q,p}(\hat{sl}(M|N))$ as one parameter deformation of the quantum superalgebra $U_q(\hat{sl}(M|N))$. For an arbitrary level $k \neq 1$ we give the bosonization of the elliptic superalgebra $U_{q,p}(\hat{sl}(1|2))$ and the screening currents that commute with $U_{q,p}(\hat{sl}(1|2))$ modulo total difference.Comment: LaTEX, 25 page

The Vertex-Face Correspondence and the Elliptic 6j-symbols

A new formula connecting the elliptic $6j$-symbols and the fusion of the vertex-face intertwining vectors is given. This is based on the identification of the $k$ fusion intertwining vectors with the change of base matrix elements from Sklyanin's standard base to Rosengren's natural base in the space of even theta functions of order $2k$. The new formula allows us to derive various properties of the elliptic $6j$-symbols, such as the addition formula, the biorthogonality property, the fusion formula and the Yang-Baxter relation. We also discuss a connection with the Sklyanin algebra based on the factorised formula for the $L$-operator.Comment: 23 page