On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains

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We study the {mathfrak{gl}}_{mmid n} XXX spin chains defined on tensor products of highest weight {mathfrak{gl}}_{mmid 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 {mathfrak{gl}}_{mmid n} Gaudin models.