Bethe Vectors for Orthogonal Integrable Models

Abstract

We consider quantum integrable models associated with the \(\mathfrak{so}_3\) algebra and describe Bethe vectors of these models in terms of the current generators of the \(\mathcal{D}Y(\mathfrak{so}_3)\) algebra. To implement this program, we use an isomorphism between the R-matrix and the Drinfeld current realizations of the Yangians and their doubles for classical type B-, C-, and D-series algebras. Using these results, we derive the actions of the monodromy matrix elements on off-shell Bethe vectors. We obtain recurrence relations for off-shell Bethe vectors and Bethe equations for on-shell Bethe vectors. The formulas for the action of the monodromy matrix elements can also be used to calculate scalar products in the models associated with the \(\mathfrak{so}_3\) algebra.