On Ginzburg's Lagrangian construction of representations of \(\text{GL}(n)\) (Q1574699)

The authors give a simpler proof of Ginzburg's result on realizations of irreducible representations of \(GL_n({\mathbf C})\) in the cohomology of certain Springer fibers for the group \(GL_d\) (for all \(d\) in \({\mathbf N})\); to be more precise, they give a simple geometric definition of the action of \(GL_n({\mathbf C})\) on the above cohomology which in turn simplifies Ginzburg's proof.