Algebraic Bethe ansatz for $\mathfrak o_{2n+1}$-invariant integrable models

We study the class of $\mathfrak o_{2n+1}$-invariant quantum integrable models in the framework of the algebraic Bethe ansatz and propose a construction of the $\mathfrak o_{2n+1}$-invariant Bethe vector in terms of the Drinfeld currents for the Yangian double $\mathcal DY(\mathfrak o_{2n+1})$. We calculate the action of the monodromy matrix elements on the off-shell Bethe vectors for these models and obtain recurrence relations for these vectors. The action formulas can be used to investigate scalar products of Bethe vectors in $\mathfrak o_{2n+1}$-invariant models.