Deformation analysis of matrix models

The Tracy-Widom equations associated with level spacing distributions are realized as a special case of monodromy preserving deformations.Comment: 23 page

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

New Integrable Lattice Models From Fuss-Catalan Algebras

We construct new trigonometric solutions of the Yang-Baxter equation, using the Fuss-Catalan algebras, a set of multi-colored versions of the Temperley-Lieb algebra, recently introduced by Bisch and Jones. These lead to new two-dimensional integrable lattice models, describing dense gases of colored loops.Comment: 30 pages, 23 eps figures, uses harvmac.tex, epsf.te

Boundary ABF Models

We diagonalise the transfer matrix of boundary ABF models using bosonized vertex operators. We compute the boundary S-matrix and check the scaling limit against known results for perturbed boundary conformal field theories.Comment: 26 pages, Latex, uses amssymbols.sty and pb-diagram.sty, 3 ps figure

Central elements of the elliptic ZnZ_n monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the $\mathbb{Z}_n$ R-matrix are studied. When the crossing parameter $w$ takes a special rational value $w=\frac{n}{N}$, where $N$ and $n$ are positive coprime integers, the center is substantially larger than that in the generic case for which the "quantum determinant" provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo.Comment: Latex file, 18 pages; V2: minor typos corrected and a reference update

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

The geometry of dual isomonodromic deformations

The JMMS equations are studied using the geometry of the spectral curve of a pair of dual systems. It is shown that the equations can be represented as time-independent Hamiltonian flows on a Jacobian bundle

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

Correlation functions of the XYZ model with a boundary

Integral formulae for the correlation functions of the XYZ model with a boundary are calculated by mapping the model to the bosonized boundary SOS model. The boundary K-matrix considered here coincides with the known general solution of the boundary Yang-Baxter equation. For the case of diagonal K-matrix, our formulae reproduce the one-point function previously obtained by solving boundary version of quantum Knizhnik-Zamolodchikov equation.Comment: 35 pages, 12 figure

Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field

Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$ chain in a constant magnetic field. For zero magnetic field, this result agrees, in both the massless and massive (anti-ferromagnetic) regimes, with the one obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra ${\cal U}_q (\hat{sl}_2)$ together with the corner transfer matrix approach (massive regime).Comment: Latex2e, 26 page