On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains

We study the $\mathfrak{gl}_{m|n}$ XXX spin chains defined on tensor products of highest $\mathfrak{gl}_{m|n}$-modules. show that on-shell Bethe vectors are eigenvectors higher transfer matrices and compute corresponding eigenvalues, confirming Conjecture 5.15 arXiv:2007.15573 extending main results arXiv:0605015 to supersymmetric case. then take classical limits obtain for Gaudin models.