43 research outputs found
Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras
We propose factorized difference operators L(u) associated with the twisted
quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}),
U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be
annihilated by a screening operator. Based on a basis of the solutions of the
difference equation L(u)w(u)=0, we also construct a Casorati determinant
solution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).Comment: 15 page
Gaudin models for gl(m|n)
Date of Acceptance: 16/04/2015We establish the basics of the Bethe ansatz for the Gaudin model associated to the Lie superalgebra gl(m|n). In particular, we prove the completeness of the Bethe ansatz in the case of tensor products of fundamental representations.Peer reviewedFinal Accepted Versio
Gaudin Model, Bethe Ansatz and Critical Level
We propose a new method of diagonalization of hamiltonians of the Gaudin
model associated to an arbitrary simple Lie algebra, which is based on Wakimoto
modules over affine algebras at the critical level. We construct eigenvectors
of these hamiltonians by restricting certain invariant functionals on tensor
products of Wakimoto modules. In conformal field theory language, the
eigenvectors are given by certain bosonic correlation functions. Analogues of
Bethe ansatz equations naturally appear as Kac-Kazhdan type equations on the
existence of certain singular vectors in Wakimoto modules. We use this
construction to expalain a connection between Gaudin's model and correlation
functions of WZNW models.Comment: 40 pages, postscript-file (references added and corrected
Heisenberg realization for U_q(sln) on the flag manifold
We give the Heisenberg realization for the quantum algebra , which
is written by the -difference operator on the flag manifold. We construct it
from the action of on the -symmetric algebra by the
Borel-Weil like approach. Our realization is applicable to the construction of
the free field realization for the [AOS].Comment: 10 pages, YITP/K-1016, plain TEX (some mistakes corrected and a
reference added
Difference Equations and Highest Weight Modules of U_q[sl(n)]
The quantized version of a discrete Knizhnik-Zamolodchikov system is solved
by an extension of the generalized Bethe Ansatz. The solutions are constructed
to be of highest weight which means they fully reflect the internal quantum
group symmetry.Comment: 9 pages, LaTeX, no figure
Note on the Algebra of Screening Currents for the Quantum Deformed W-Algebra
With slight modifications in the zero modes contributions, the positive and
negative screening currents for the quantum deformed W-algebra W_{q,p}(g) can
be put together to form a single algebra which can be regarded as an elliptic
deformation of the universal enveloping algebra of \hat{g}, where g is any
classical simply-laced Lie algebra.Comment: LaTeX file, 9 pages. Errors in Serre relation corrected. Two
references to Awata,H. et al adde
Difference L operators related to q-characters
We introduce a factorized difference operator L(u) annihilated by the
Frenkel-Reshetikhin screening operator for the quantum affine algebra
U_q(C^{(1)}_n). We identify the coefficients of L(u) with the fundamental
q-characters, and establish a number of formulas for their higher analogues.
They include Jacobi-Trudi and Weyl type formulas, canceling tableau sums,
Casorati determinant solution to the T-system, and so forth. Analogous
operators for the orthogonal series U_q(B^{(1)}_n) and U_q(D^{(1)}_n) are also
presented.Comment: 25 pages, LaTeX2e, no figur
H(3)+ correlators from Liouville theory
We prove that arbitrary correlation functions of the H(3)+ model on a sphere
have a simple expression in terms of Liouville theory correlation functions.
This is based on the correspondence between the KZ and BPZ equations, and on
relations between the structure constants of Liouville theory and the H(3)+
model. In the critical level limit, these results imply a direct link between
eigenvectors of the Gaudin Hamiltonians and the problem of uniformization of
Riemann surfaces. We also present an expression for correlation functions of
the SL(2)/U(1) coset model in terms of correlation functions in Liouville
theory.Comment: 24 pages, v3: minor changes, references adde
Form factors of boundary fields for A(2)-affine Toda field theory
In this paper we carry out the boundary form factor program for the
A(2)-affine Toda field theory at the self-dual point. The latter is an
integrable model consisting of a pair of particles which are conjugated to each
other and possessing two bound states resulting from the scattering processes 1
+1 -> 2 and 2+2-> 1. We obtain solutions up to four particle form factors for
two families of fields which can be identified with spinless and spin-1 fields
of the bulk theory. Previously known as well as new bulk form factor solutions
are obtained as a particular limit of ours. Minimal solutions of the boundary
form factor equations for all A(n)-affine Toda field theories are given, which
will serve as starting point for a generalisation of our results to higher rank
algebras.Comment: 24 pages LaTeX, 1 figur