Quantum Affine Symmetry in Vertex Models

Abstract. Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations. The main relations among them are the difference equations obtained from the qKZ equation by specializing the variables (λ 1 , · · · , λ 2n ) as (λ 1 , · · · , λ n , λ n + 1, · · · , λ 1 + 1). We call it the reduced qKZ equation. In this article we construct a special family of solutions to this system. They can be written as linear combinations of products of two transcendental functionsω, ω with coefficients being rational functions. We show that correlation functions of the XXZ model in the massive regime are given by these formulas with an appropriate choice ofω, ω. We also present a conjectural formula in the massless regime.

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“…These equations arise as ones satisfied by the correlation functions of the XXZ model [10]. We review this connection in Section 13.…”

Section: Reduced Qkz Equationmentioning

confidence: 99%

Reduced qKZ Equation and Correlation Functions of the XXZ Model

Boos

Jimbo

Miwa

et al. 2005

Commun. Math. Phys.

122

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“…We shall follow the convention of [11] concerning U q ( sl 2 ). In particular, on the Chevalley generators e i , f i , t i = q h i (i = 0, 1) and q d , the coproduct is chosen to be…”

Section: A Trigonometric Casementioning

confidence: 99%

Notes on Highest Weight Modules of the Elliptic Algebra $\mathfrak{A}_{q, p}(\hat{sl_2})$

Foda¹,

Iohara

Jimbo

et al. 1995

Prog. Theor. Phys. Suppl.

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We discuss a construction of highest weight modules for the recently defined elliptic algebra A q,p ( sl 2 ), and make several conjectures concerning them. The modules are generated by the action of the components of the operator L on the highest weight vectors. We introduce the vertex operators Φ and Ψ * through their commutation relations with the L-operator. We present ordering rules for the Land Φ-operators and find an upper bound for the number of linearly independent vectors generated by them, which agrees with the known characters of sl 2 -modules. IntroductionIn our previous paper [1] we defined the elliptic quantum affine algebra A q,p (ĝ) with g = gl 2 or sl 2 . The present paper is an attempt toward understanding the correct elliptic analogues of the highest weight modules and vertex operators. Our aim here is to present conjectures concerning their existence and expected properties, along with some experimental computations to support them. *

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“…For U q ( sl 2 ), the formulas for the W -factors in the simplest case can be found e.g. in [62]. The 'dressed' VO's satisfy similar relations with appropriate dynamical shift.…”

Section: Dynamical Rll-relations and Vertex Operatorsmentioning

confidence: 96%

“…Connection matrix of their solutions gives a face type elliptic solution of YBE. See [61,87,88,16,62]. massive integrable models : Integrable perturbations of CFT were studied in [12,13,14,15] and (1, 3)-perturbed CFT is described by the sine-Gordon model.…”

Section: Deformed W Algebras (Dwa's)mentioning

confidence: 99%