Free Field Realization of Vertex Operators for Level Two Modules of Uq(sl(2)^)U_q(\hat{sl(2)})

Free field relization of vertex operators for lvel two modules of $U_q(\hat{sl(2)})$ is shown through the free field relization of the modules given by Idzumi in Ref.[4,5]. We constructed types I and II vertex operators when the spin of the addociated evaluation modules is 1/2 and typ II's for the spin 1.Comment: 15 pages, to appear in J.Phys.A:Math and Genera

Impurity Operators in RSOS Models

We give a construction of impurity operators in the `algebraic analysis' picture of RSOS models. Physically, these operators are half-infinite insertions of certain fusion-RSOS Boltzmann weights. They are the face analogue of insertions of higher spin lines in vertex models. Mathematically, they are given in terms of intertwiners of $U(\hat{sl}_2)_q$ modules. We present a detailed perturbation theory check of the conjectural correspondence between the physical and mathematical constructions in a particular simple example.Comment: Latex, 24 pages, uses amsmath, amsthm, amssymb, epic, eepic and texdraw style files (Minor typos corrected) (minor changes

Mixing of Ground States in Vertex Models

We consider the analogue of the 6-vertex model constructed from alternating spin n/2 and spin m/2 lines, where $1\leq n<m$. We identify the transfer matrix and the space on which it acts in terms of the representation theory of $U_q(sl_2)$. We diagonalise the transfer matrix and compute the S-matrix. We give a trace formula for local correlation functions. When n=1, the 1-point function of a spin m/2 local variable for the alternating lattice with a particular ground state is given as a linear combination of the 1-point functions of the pure spin m/2 model with different ground states. The mixing ratios are calculated exactly and are expressed in terms of irreducible characters of $U_q(sl_2)$ and the deformed Virasoro algebra.Comment: 12 pages, LaTeX, typos correcte

Quantum R-matrix and Intertwiners for the Kashiwara Algebra

We study the algebra $B_q(\ge)$ presented by Kashiwara and introduce intertwiners similar to $q$-vertex operators. We show that a matrix determined by 2-point functions of the intertwiners coincides with a quantum R-matrix (up to a diagonal matrix) and give the commutation relations of the intertwiners. We also introduce an analogue of the universal R-matrix for the Kashiwara algebra.Comment: 21 page

Correlation functions of the higher spin XXX chains

Using the Algebraic Bethe Ansatz we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin $\frac 12$ Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can be considered in the framework of this approach in the thermodynamic limit. Finally, a multiple integral representation for the spin 1 zero temperature correlation functions is obtained in the thermodynamic limit.Comment: LaTeX, 23 pages, replaced with a revised versio

Fusion of the qq-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

Free Boson Representation of Uq(sl^3)U_q(\widehat{sl}_3)

A representation of the quantum affine algebra $U_{q}(\widehat{sl}_3)$ of an arbitrary level $k$ is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in the $q \rightarrow 1$ limit. The analogues of the screening currents are also obtained. They commute with the action of $U_{q}(\widehat{sl}_3)$ modulo total differences of some fields.Comment: 12 pages, LaTeX, RIMS-920, YITP/K-101

Crystalizing the Spinon Basis

The quasi-particle structure of the higher spin XXZ model is studied. We obtained a new description of crystals associated with the level $k$ integrable highest weight $U_q(\widehat{sl_2})$ modules in terms of the creation operators at $q=0$ (the crystaline spinon basis). The fermionic character formulas and the Yangian structure of those integrable modules naturally follow from this description. We have also derived the conjectural formulas for the multi quasi-particle states at $q=0$.Comment: 25 pages, late

Level-one Highest Weight Representation of Uq[sl(N∣1)^]U_q[\hat{sl(N|1)}] and Bosonization of the Multi-component Super t-J Model

We study the level-one irreducible highest weight representations of the quantum affine superalgebra $U_q[\hat{sl(N|1)}]$, and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible $U_q[\hat{sl(N|1)}]$-modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multi-component super $t-J$ model by using the bosonized vertex operators.Comment: LaTex file 21 page

Hirota equation as an example of integrable symplectic map

The hamiltonian formalism is developed for the sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of the corresponding classical finite-dimensional system is established.Comment: 10 pages, LaTe