1,856 research outputs found

### The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra

After reviewing the recent results on the Drinfeld realization of the face
type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra
U_{q,p}(sl_N^), we investigate a fusion of the vertex operators of
U_{q,p}(sl_N^). The basic generating functions \Lambda_j(z) (j=1,2,.. N-1) of
the deformed W_N algebra are derived explicitly.Comment: 15 pages, to appear in Journal of physics A special issue - RAQIS0

### Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations

The Hamiltonian approach to the theory of dual isomonodromic deformations is
developed within the framework of rational classical R-matrix structures on
loop algebras. Particular solutions to the isomonodromic deformation equations
appearing in the computation of correlation functions in integrable quantum
field theory models are constructed through the Riemann-Hilbert problem method.
The corresponding $\tau$-functions are shown to be given by the Fredholm
determinant of a special class of integral operators.Comment: LaTeX 13pgs (requires lamuphys.sty). Text of talk given at workshop:
Supersymmetric and Integrable Systems, University of Illinois, Chicago
Circle, June 12-14, 1997. To appear in: Springer Lecture notes in Physic

### On representations of the elliptic quantum group $E_{\tau,\eta}(sl_2)$

We describe representation theory of the elliptic quantum group
$E_{\tau,\eta}(sl_2)$. It turns out that the representation theory is parallel
to the representation theory of the Yangian $Y(sl_2)$ and the quantum loop
group $U_q(\widetilde { sl }_2)$.Comment: 21 pages, amstex. An explicit formula for the general R matrix is
given in this revised versio

### The 19-Vertex Model at critical regime $|q|=1$

We study the 19-vertex model associated with the quantum group
$U_q(\hat{sl_2})$ at critical regime $|q|=1$. We give the realizations of the
type-I vertex operators in terms of free bosons and free fermions. Using these
free field realizations, we give the integral representations for the
correlation functions.Comment: LaTEX2e, 19page

### Fermionic screening operators in the sine-Gordon model

Extending our previous construction in the sine-Gordon model, we show how to
introduce two kinds of fermionic screening operators, in close analogy with
conformal field theory with c<1.Comment: 18 pages, 1 figur

### The Monodromy Matrices of the XXZ Model in the Infinite Volume Limit

We consider the XXZ model in the infinite volume limit with spin half quantum
space and higher spin auxiliary space. Using perturbation theory arguments, we
relate the half infinite transfer matrices of this class of models to certain
$U_q(\hat{sl_2})$ intertwiners introduced by Nakayashiki. We construct the
monodromy matrices, and show that the one with spin one auxiliary space gives
rise to the L operator.Comment: 19 page

### Free field constructions for the elliptic algebra ${\cal A}_{q,p}(\hat{sl}_2)$ and Baxter's eight-vertex model

Three examples of free field constructions for the vertex operators of the
elliptic quantum group ${\cal A}_{q,p}(\hat{sl}_2)$ are obtained. Two of these
(for $p^{1/2}=\pm q^{3/2},p^{1/2}=-q^2$) are based on representation theories
of the deformed Virasoro algebra, which correspond to the level 4 and level 2
$Z$-algebra of Lepowsky and Wilson. The third one ($p^{1/2}=q^{3}$) is
constructed over a tensor product of a bosonic and a fermionic Fock spaces. The
algebraic structure at $p^{1/2}=q^{3}$, however, is not related to the deformed
Virasoro algebra. Using these free field constructions, an integral formula for
the correlation functions of Baxter's eight-vertex model is obtained. This
formula shows different structure compared with the one obtained by Lashkevich
and Pugai.Comment: 23 pages. Based on talks given at "MATHPHYS ODYSSEY 2001-Integrable
Models and Beyond" at Okayama and Kyoto, February 19-23, 2001, et

### Fusion of the $q$-Vertex Operators and its Application to Solvable Vertex Models

We diagonalize the transfer matrix of the inhomogeneous vertex models of the
6-vertex type in the anti-ferroelectric regime intoducing new types of q-vertex
operators. The special cases of those models were used to diagonalize the s-d
exchange model\cite{W,A,FW1}. New vertex operators are constructed from the
level one vertex operators by the fusion procedure and have the description by
bosons. In order to clarify the particle structure we estabish new isomorphisms
of crystals. The results are very simple and figure out representation
theoretically the ground state degenerations.Comment: 35 page

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