Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · q-alg/9709028

8-Vertex Correlation Functions and Twist Covariance of q-KZ Equation

C. Fronsdal·A. Galindo
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the vertex operators $Φ(z)$ associated with standard quantum groups. The element $Z = RR^{t}$ is a "Casimir operator" for quantized Kac-Moody algebras and the quantum Knizhnik-Zamolodchikov (q-KZ) equation is interpreted as the statement $:ZΦ(z): = Φ(z)$. We study the covariance of the q-KZ equation under twisting, first within the category of Hopf algebras, and then in the wider context of quasi Hopf algebras. We obtain the intertwining operators associated with the elliptic R-matrix and calculate the two-point correlation function for the eight-vertex model.

Explore related subjects

q-algmath.QA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C. Fronsdal, A. Galindo. 1997-09-18. 8-Vertex Correlation Functions and Twist Covariance of q-KZ Equation. https://doi.org/10.1142/s0129055x98000331

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2023

On Irreducibility of Tensor Products of Yangian Modules

We study the tensor product $V$ of any number of "elementary" irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by a complex parameter, and contains a vector called singular. We give sufficient conditions for cyclicity in $V$ of the tensor product of these singular vectors. By using this result, we give an irreducibility criterion for $V$ when each of the skew Young diagrams determining the tensor factors has rectangular shape.

q-alg↗
arXiv2022

On the parametrization of solutions of the Yang--Baxter equations

We study all five-, six-, and one eight-vertex type two-state solutions of the Yang-Baxter equations in the form $A_{12} B_{13} C_{23} = C_{23} B_{13} A_{12}$, and analyze the interplay of the `gauge' and `inversion' symmetries of these solution. Starting with algebraic solutions, whose parameters have no specific interpretation, and then using these symmetries we can construct a parametrization where we can identify global, color and spectral parameters. We show in particular how the distribution of these parameters may be changed by a change of gauge.

q-alg↗
arXiv2020

Higher-Dimensional Algebra I: Braided Monoidal 2-Categories

We begin with a brief sketch of what is known and conjectured concerning braided monoidal 2-categories and their applications to 4d topological quantum field theories and 2-tangles (surfaces embedded in 4-dimensional space). Then we give concise definitions of semistrict monoidal 2-categories and braided monoidal 2-categories, and show how these may be unpacked to give long explicit definitions similar to, but not quite the same as, those given by Kapranov and Voevodsky. Finally, we describe how to construct a semistrict braided monoidal 2-category Z(C) as the `center' of a semistrict monoidal category C. This is analogous to the construction of a braided monoidal category as the center, or `quantum double', of a monoidal category. As a corollary, our construction yields a strictification theorem for braided monoidal 2-categories.

q-alg↗