Examples of Hamiltonian minimal lagrangian submanifolds in ${\rm Gr} (r, n)$

In the paper one presents a generalization of A.E. Mironov construction of Hamiltonian minimal and minimal lagrangian submanifolds to the case of an algebraic variety which admits a Kahler - Einstein metric, symmetric with respect to a toric action of $T^k$. As an application one presents examples of Hamiltonian minimal lagrangian submanifolds in the Grassmanian ${\rm Gr}(r, n)$.