853 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
Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model
Belavin's -symmetric model is considered on the
basis of bosonization of vertex operators in the model and
vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of
-symmetric model and tail operators are expressed in
terms of bosonized vertex operators in the model. Correlation
functions of -symmetric model can be obtained by
using these objects, in principle. In particular, we calculate spontaneous
polarization, which reproduces the result by myselves in 1993.Comment: For the next thirty days the full text of this article is available
at http://stacks.iop.org/1751-8121/42/16521
Form factors and action of U_{\sqrt{-1}}(sl_2~) on infinite-cycles
Let be a sequence of
skew-symmetric polynomials in satisfying , whose coefficients are symmetric Laurent polynomials in . We
call an -cycle if
holds for all .
These objects arise in integral representations for form factors of massive
integrable field theory, i.e., the SU(2)-invariant Thirring model and the
sine-Gordon model. The variables are the integration
variables and are the rapidity variables. To each
-cycle there corresponds a form factor of the above models.
Conjecturally all form-factors are obtained from the -cycles.
In this paper, we define an action of
on the space of -cycles.
There are two sectors of -cycles depending on whether is even or
odd. Using this action, we show that the character of the space of even (resp.
odd) -cycles which are polynomials in is equal to the
level irreducible character of with lowest
weight (resp. ). We also suggest a possible tensor
product structure of the full space of -cycles.Comment: 27 pages, abstract and section 3.1 revise
Algebraic representation of correlation functions in integrable spin chains
Taking the XXZ chain as the main example, we give a review of an algebraic
representation of correlation functions in integrable spin chains obtained
recently. We rewrite the previous formulas in a form which works equally well
for the physically interesting homogeneous chains. We discuss also the case of
quantum group invariant operators and generalization to the XYZ chain.Comment: 31 pages, no figur
The Vertex-Face Correspondence and the Elliptic 6j-symbols
A new formula connecting the elliptic -symbols and the fusion of the
vertex-face intertwining vectors is given. This is based on the identification
of the fusion intertwining vectors with the change of base matrix elements
from Sklyanin's standard base to Rosengren's natural base in the space of even
theta functions of order . The new formula allows us to derive various
properties of the elliptic -symbols, such as the addition formula, the
biorthogonality property, the fusion formula and the Yang-Baxter relation. We
also discuss a connection with the Sklyanin algebra based on the factorised
formula for the -operator.Comment: 23 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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