46 research outputs found
Yangian Algebras and Classical Riemann Problems
We investigate different Hopf algebras associated to Yang's solution of
quantum Yang-Baxter equation. It is shown that for the precise definition of
the algebra one needs the commutation relations for the deformed algebra of
formal currents and the specialization of the Riemann problem for the currents.
Two different Riemann problems are considered. They lead to the central
extended Yangian double associated with and to the degeneration of
scaling limit of elliptic affine algebra. Unless the defining relations for the
generating functions of the both algebras coincide their properties and the
theory of infinite-dimensional representations are quite different. We discuss
also the Riemann problem for twisted algebras and for scaled elliptic algebra.Comment: 36 pages, 3 figures under bezier.sty, corrected some typo
Generating Series for Nested Bethe Vectors
We reformulate nested relations between off-shell Uq(^glN) Bethe vectors as a certain equation on generating series of strings of the composed Uq(^glN) currents. Using inversion of the generating series we find a new type of hierarchical relations between universal off-shell Bethe vectors, useful for a derivation of Bethe equation. As an example of application, we use these relations for a derivation of analytical Bethe ansatz equations [Arnaudon D. et al., Ann. Henri Poincaré 7 (2006), 1217-1268, math-ph/0512037] for the parameters of universal Bethe vectors of the algebra Uq(^gl2)
Off-shell Bethe vectors and Drinfeld currents
In this paper we compare two constructions of weight functions (off-shell
Bethe vectors) for the quantum affine algebra . The
first construction comes from the algebraic nested Bethe ansatz. The second one
is defined in terms of certain projections of products of Drinfeld currents. We
show that two constructions give the same result in tensor products of vector
representations of .Comment: 25 pages, misprints correcte
Bethe Ansatz for the Universal Weight Function
We consider universal off-shell Bethe vectors given in terms of Drinfeld
realization of the algebra
[arXiv:math/0610517,arXiv:0711.2819]. We investigate ordering properties of the
product of the transfer matrix and these vectors.
We derive that these vectors are eigenvectors of the transfer matrix if their
Bethe parameters satisfy the universal Bethe equations [arXiv:math-ph/0512037].Comment: 31 pages, 1 figure, misprints corrected and reference adde