Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9211087 · Progress of Theoretical Physics

Exchange Relations for the q-Vertex Operators of Uq(\widehatsl2)

H. Awata

Published Apr 1, 1993• 0 citations
arXivHTMLPDF

Abstract

We consider the q -deformed Knizhnik-Zamolodchikov equation for the two point function of q -deformed vertex operators of Uq (\widehat sl2 ). We give explicitly the fundamental solutions, the connection matrices and the exchange relations for the q -vertex operators of spin 1/2 and j ∈ (1/2) Z≥0 . Consequently, we confirm that the connection matrices are equivalent to the elliptic Boltzmann weights of IRF type obtained by the fusion procedure from ABF models.

DOI
10.1143/ptp/89.4.771

Related papers

Exchange Relations for the q-Vertex Operators of $U_{q}(\widehat{sl_{2}})$

Hidetoshi Awata

We consider the q -deformed Knizhnik-Zamolodchikov equation for the two point function of q -deformed vertex operators of Uq (\widehat sl2 ). We give explicitly the fundamental solutions, the connection matrices and the exchange relations for the q -vertex operators of spin 1/2 and j ∈ (1/2) Z≥0 . Consequently, we confirm that the connection matrices are equivalent to the elliptic Boltzmann weights of IRF type obtained by the fusion procedure from ABF models.

Progress of Theoretical Physics•Apr 1, 1993•0 citations

Theta function solutions of the quantum Knizhnik–Zamolodchikov–Bernard equation for a face model

Peter E. Finch, Robert Weston, Paul Zinn-Justin

Abstract We consider the quantum Knizhnik–Zamolodchikov–Bernard equation for a face model with elliptic weights, the SOS model. We provide explicit solutions as theta functions. On the so-called combinatorial line, in which the model is equivalent to the three-colour model , these solutions are shown to be eigenvectors of the transfer matrix with periodic boundary conditions.

Journal of Physics A Mathematical and Theoretical•Jan 5, 2016•2 citations

Theta function solutions of the qKZB equation for a face model

Peter E. Finch, Robert Weston, Paul Zinn-Justin

We consider the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model with elliptic weights, the SOS model. We provide explicit solutions as theta functions. On the so-called combinatorial line, in which the model is equivalent to the three-colour model, these solutions are shown to be eigenvectors of the transfer matrix with periodic boundary conditions.

arXiv:1509.04594•Sep 15, 2015•2 citations

SOME INTEGRAL FORMULAS FOR THE SOLUTIONS OF THE sl 2 dKZ EQUATION WITH LEVEL −4

Atsushi Nakayashiki

A direct proof is given for the fact that the integral formula for the XXX limit of the trace of the type I q-vertex operators satisfies the deformed Knizhnik-Zamolodchikov (dKZ) equation with level −4. We have also carried out one-time integration by taking the residue at infinity. As a corollary of these we can construct a family of the integral formulas for solutions to the dKZ equation. Another corollary is the integral formula for the correlation function of the inhomogeneous XXX model, whose number of integrals is less than that of the previously obtained correlator for the XXZ model.

International Journal of Modern Physics A•Dec 30, 1994•30 citations

SU(2) parameterisation of Baxter's model

Omar E. Foda

A parametrisation of the Boltzmann weights of Baxter's symmetric eight-vertex model (1982) is derived, using Cherednik's representation (1979) of the Zamolodchikov algebra, in terms of theta functions based on the weight lattice of SU(2). The Yang-Baxter equations are satisfied as a consequence of the associativity of the Zamolodchikov algebra. The derivation makes the connection of Baxter's model to the spin-1/2 representation of SU(2) explicit.

Journal of Physics A Mathematical and General•Jul 21, 1990•0 citations

FUSION HIERARCHY AND FINITE-SIZE CORRECTIONS OF Uq[sl(2)] INVARIANT VERTEX MODELS WITH OPEN BOUNDARIES

The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices satisfy a group of functional relations, which are the su(2) fusion rule held by the transfer matrices of the fused models. The fused transfer matrices form a commuting family and also commute with the quantum group Uq[sl(2)]. In the case of the parameter qh = −1 (h = 4,5, · · ·) the functional relations in the limit of spectral parameter u → i ∞ are truncated. This shows that the su(2) fusion rule with finite level appears for the six vertex model with the open boundary conditions. We have solved the functional relations to obtain the finite-size corrections of the fused transfer matrices for low-lying excitations. From the corrections the central charges and conformal weights of underlying conformal field theory are extracted. To see different boundary conditions we also have studied the six-vertex model with a twisted boundary condition. hep-th/9502053; to appear in NPB. 1

•Jan 1, 1995•0 citations
We consider the q -deformed Knizhnik-Zamolodchikov equation for the two point function of q -deformed vertex operators of Uq (\widehat sl2 ). We give explicitly the fundamental solutions, the connection matrices and the exchange relations for the q -vertex operators of spin 1/2 and j ∈ (1/2) Z≥0 . Consequently, we confirm that the connection matrices are equivalent to the elliptic Boltzmann weights of IRF type obtained by the fusion procedure from ABF models.
Exchange Relations for the q-Vertex Operators of Uq(sl2^)U_{q}(\widehat{sl_{2}})Uq​(sl2​​)
A direct proof is given for the fact that the integral formula for the XXX limit of the trace of the type I q-vertex operators satisfies the deformed Knizhnik-Zamolodchikov (dKZ) equation with level −4. We have also carried out one-time integration by taking the residue at infinity. As a corollary of these we can construct a family of the integral formulas for solutions to the dKZ equation. Another corollary is the integral formula for the correlation function of the inhomogeneous XXX model, whose number of integrals is less than that of the previously obtained correlator for the XXZ model.
The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices satisfy a group of functional relations, which are the su(2) fusion rule held by the transfer matrices of the fused models. The fused transfer matrices form a commuting family and also commute with the quantum group Uq[sl(2)]. In the case of the parameter qh = −1 (h = 4,5, · · ·) the functional relations in the limit of spectral parameter u → i ∞ are truncated. This shows that the su(2) fusion rule with finite level appears for the six vertex model with the open boundary conditions. We have solved the functional relations to obtain the finite-size corrections of the fused transfer matrices for low-lying excitations. From the corrections the central charges and conformal weights of underlying conformal field theory are extracted. To see different boundary conditions we also have studied the six-vertex model with a twisted boundary condition. hep-th/9502053; to appear in NPB. 1