Rectangular Yang-Baxter algebras and alternating A-type integrable vertex models

SERGIO GRILLO; HUGO MONTANI

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Año: 2005 p. 1 - 18

0219-8878

Given a couple of Yang-Baxter operators R^{k} and R^{l} corresponding to integrable anisotropic vertex models of A_{k-1} and A_{l-1} type, respectively, we construct and study a class of related lattice models whose monodromy matrices alternate mentioned operators. In order to do that, we use a natural generalization of the idea of coproduct in a bialgebra, that appears in the scenario of non commutative algebraic geometry, related to the notion of internal homomorphisms of quantum spaces. We build up all eigenstates and eigenvalues of the transfer matrix by means of algebraic Bethe ansatz technics, where not only one vector, but a pseudovacuum subspace is needed for the process of diagonalization.