Kei Miki

Correlation functions of the XXZ model for Δ < − 1

Abstract A new approach to the correlation functions is presented for the XXZ model in the antiferroelectric regime. The method is based on the recent realization of the quantum affine symmetry using vertex operators. With the aid of a boson representation for the latter, an integral formula is found for correlation functions of arbitrary local operators. As a special case it reproduces the spontaneous staggered polarization obtained earlier by Baxter.

A (q,γ) analog of the W1+∞ algebra

A (q,γ) analog of the W1+∞ algebra is introduced. Irreducible quasifinite highest weight modules of this algebra and R matrices acting on a tensor product of these modules are investigated. A connection with the q deformed Virasoro and WN algebras is also discussed.

Vertex operators in solvable lattice models

The basic properties of q‐vertex operators are formulated in the context of the Andrews–Baxter–Forrester (ABF) series, as an example of face interaction models, the q‐difference equations satisfied by their correlation functions are derived, and their connection with representation theory established. The q‐difference equations of the Kashiwara–Miwa (KM) series are discussed as an example of edge interaction models. Next, the Ising model, the simplest special case of both ABF and KM series, is studied in more detail using the Jordan–Wigner fermions. In particular, all matrix elements of vertex operators are calculated.

The representation theory of the SO(3) invariant superconformal algebra

The representation theory of the SO(3) invariant superconformal algebra is discussed. The necessary and sufficient condition of unitarity, the Kac determinants, the character formulae for unitary representations and their modular transformation laws are obtained under some assumptions.

Creation/annihilation operators and form factors of the XXZ model

Abstract Two kinds of creation/annihilation operators for the XXZ model in the antiferroelectric regime are constructed. They pressumably have a well defined low temperature limit. As an application, the axioms of form factors are discussed.

Representations of quantum toroidal algebra Uq(sln+1,tor) (n⩾2)

By the method of Chari and Pressley, representations of the quantum toroidal algebra Uq(sln+1,tor) (n⩾2) are studied.

Toroidal Braid Group Action and an Automorphism of Toroidal Algebra Uq(sln+1,tor) (n ≥ 2)

Utilizing an action of a modification of the double affine Hecke braid group of type gln+1, we obtain an automorphism of the toroidal algebra Uq(sln+1) (n ≥ 2), which maps two central elements C and k0 · kn to k0 · kn and C−1, respectively.

Quantum toroidal algebra Uq(sl2,tor) and R matrices

We show the existence of R matrices acting on the tensor product of a certain class of representations of the quantum toroidal algebra Uq(sl2,tor). In particular, the explicit expressions of R matrices acting on the tensor product of level 1 integrable highest weight representations of Uq(sl2∧) are obtained. Our approach is based on the work of Chari and Pressley.

MEAN STAGGERED POLARIZATION FOR THE HIGHER SPIN ANALOG OF THE 6-VERTEX MODEL

We compute the mean staggered polarization of the vertex models corresponding to higher spin representations of

L operators and Drinfeld’s generators

U_q({\widehat{\mathfrak{sl}}}_2)