On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains

Abstract We study the gl m ∣ n $$ {\mathfrak{gl}}_{m\mid n} $$ XXX spin chains defined on tensor products of highest weight gl m ∣ n $$ {\mathfrak{gl}}_{m\mid n} $$ -modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues. Then we take the classical limits and obtain the corresponding results for the gl m ∣ n $$ {\mathfrak{gl}}_{m\mid n} $$ Gaudin models.