1,211 research outputs found
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 -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
Free field constructions for the elliptic algebra and Baxter's eight-vertex model
Three examples of free field constructions for the vertex operators of the
elliptic quantum group are obtained. Two of these
(for ) are based on representation theories
of the deformed Virasoro algebra, which correspond to the level 4 and level 2
-algebra of Lepowsky and Wilson. The third one () is
constructed over a tensor product of a bosonic and a fermionic Fock spaces. The
algebraic structure at , 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
Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators
We investigate the structure of the elliptic algebra U_{q,p}(^sl_2)
introduced earlier by one of the authors. Our construction is based on a new
set of generating series in the quantum affine algebra U_q(^sl_2), which are
elliptic analogs of the Drinfeld currents. They enable us to identify
U_{q,p}(^sl_2) with the tensor product of U_q(^sl_2) and a Heisenberg algebra
generated by P,Q with [Q,P]=1. In terms of these currents, we construct an L
operator satisfying the dynamical RLL relation in the presence of the central
element c. The vertex operators of Lukyanov and Pugai arise as `intertwiners'
of U_{q,p}(^sl_2) for level one representation, in the sense to be elaborated
on in the text. We also present vertex operators with higher level/spin in the
free field representation.Comment: 49 pages, (AMS-)LaTeX ; added an explanation of integration contours;
added comments. To appear in Comm. Math. Phys. Numbering of equations is
correcte
Generalized Kontsevich Model Versus Toda Hierarchy and Discrete Matrix Models
We represent the partition function of the Generalized Kontsevich Model (GKM)
in the form of a Toda lattice -function and discuss various implications
of non-vanishing "negative"- and "zero"-time variables: the appear to modify
the original GKM action by negative-power and logarithmic contributions
respectively. It is shown that so deformed -function satisfies the same
string equation as the original one. In the case of quadratic potential GKM
turns out to describe {\it forced} Toda chain hierarchy and, thus, corresponds
to a {\it discrete} matrix model, with the role of the matrix size played by
the zero-time (at integer positive points). This relation allows one to discuss
the double-scaling continuum limit entirely in terms of GKM, essentially
in terms of {\it finite}-fold integrals.Comment: 46
Fusion of the -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 Field Approach to the Dilute A_L Models
We construct a free field realization of vertex operators of the dilute A_L
models along with the Felder complex. For L=3, we also study an E_8 structure
in terms of the deformed Virasoro currents.Comment: (AMS-)LaTeX(2e), 43page
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