The Vertex - Face Correspondence and the Elliptic 6 j - symbols
نویسنده
چکیده
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.
منابع مشابه
ELLIPTIC INTEGRABLE SYSTEMS Generalised Elliptic 6j-Symbols in Terms of the Vertex-Face Intertwining Vectors
We review a recent result on a formula of the generalized elliptic 6j-symbols expressed in terms of the fusion of the vertex-face intertwining vectors. The formula is derived by identifying 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. We also give a list of ex...
متن کاملThe Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism
Based on the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the k × k fusion eight-vertex model in terms of the corresponding fusion SOS model. Here k ∈ Z>0. A general formula for correlation functions is derived as a trace over the space of states of lattice operators such as the corner transfer matrices, the half transfer matrices (vertex ope...
متن کاملFusion of Baxter’s Elliptic R-matrix and the Vertex-Face Correspondence
The matrix elements of the 2× 2 fusion of Baxter’s elliptic R-matrix, R(u), are given explicitly. Based on a note by Jimbo, we give a formula which show that R(u) is gauge equivalent to Fateev’s R-matrix for the 21-vertex model. Then the crossing symmetry formula for R(u) is derived. We also consider the fusion of the vertex-face correspondence relation and derive a crossing symmetry relation b...
متن کاملDynamically twisted algebra Aq,p;π̂(ĝl2) as current algebra generalizing screening currents of q-deformed Virasoro algebra
In this paper, we propose an elliptic algebra Aq,p;π̂(ĝl2) which is based on the relations RLL = LLR, where R and R are the dynamical R-maxtrices of A (1) 1 type face model with the elliptic moduli shifted by the center of the algebra. From the Ding-Frenkel correspondence , we find that its corresponding (Drinfeld) current algebra at level one is the algebra of screening currents for qdeformed V...
متن کاملThe elliptic algebra Uq,p( ̂ slN ) and the deformation of the WN algebra
After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group Bq,λ(ŝlN ) by the elliptic algebra Uq,p(ŝlN ), we investigate a fusion of the vertex operators of Uq,p(ŝlN ). The basic generating functions Λj(z) (1 ≤ j ≤ N − 1) of the deformed WN algebra are derived explicitly.
متن کامل