Bezrukavnikov and Ginzburg have unpublished notes, 'Hilbert Schemes and Reductive Groups' (referenced here, for example): does anyone know what became of these notes? Did Bezrukavnikov-Ginzburg publish anything based on these notes? I am interested in finding them as it is claimed (in the reference linked to above) that Bezrukavnikov-Ginzburg obtain an isomorphism between equivariant K-theory of $X^{n}$ ($X$ a quasi-projective smooth surface) and cohomology of $X^{[n]}$ (Hilbert scheme of $n$ points on $X$); this should(?) allow an interpretation of the Nakajima-Grojnowski construction of the Heisenberg algebra via equivariant K-theory.

Thanks in advance.

Representation Theory, with a somewhat related title "Cherednik algebras and Hilbert schemes in characteristic p" (maybe not related to your concerns). You might do best to contact the authors (or Weiqiang Wang) directly, unless someone has a quick answer for your more detailed question. – Jim Humphreys Feb 25 '13 at 1:28