Quantum Affine Algebras and Integrable Quantum Systems

Mo‐Lin Ge

Niklas Beisert, W. Galléas, Takuya Matsumoto

The integrable structure of the one-dimensional Hubbard model is based on Shastry's R -matrix and the Yangian of a centrally extended superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R -matrix has recently been found. This R -matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine algebra in two special limits.

S. Belliard

An integral presentation for the scalar products of nested Bethe vectors for the quantum integrable models associated with the quantum affine algebra U q ( gl 3 ) is given.This result is obtained in the framework of the universal Bethe ansatz, using presentation of the universal Bethe vectors in terms of the total currents of a "new" realization of the quantum affine algebra U q ( gl 3 ).

L. Frappat, P. Sorba, A. Sciarrino +1 more

L. Frappat, A. Sciarrino, S. Sciuto +1 more