On Ginzburg's Lagrangian construction of representations of GL(n)

In [3] V. Ginzburg observed that one can realize irreducible representation s of the group GL(n, C) in the cohomology of certain Springer's fibers for the group GL(d) (for all d is an element of n). However, Ginzburg's constru ction of the action of GL(n) on this cohomology was a bit artificial the de fined the action of Chevalley generators of the Lie algebra gl(n) on the co rresponding cohomology by certain explicit correspondences, following the w ork of A. Beilinson, G. Lusztig and R. MacPherson ([1]), who gave a similar construction of the quantum group U-q(gl(n))). In this note we give a very simple geometric definition of the action of th e whole group GL(n, C) on the above cohomology and simplify the results of [3].