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Jun 15, 2011 at 1:37 comment added Joel Kamnitzer There is a famous paper by Beilinson, Lusztig, and MacPherson where they develop this idea of constructing representations of quantum groups using $\mathbb F_q $ points of partial flag varieties.
Nov 16, 2009 at 4:45 comment added Ben Webster This is closely related to the Hall algebra stuff I mentioned earlier. I don't know anywhere this is properly written down, but it should be easy to just do Ginzburg's proof a little more carefully. I'll note, this really the decategorification of the Kac-Moody 2-category action on perverse sheaves on those flag varieties, so its implicit in that.
Nov 15, 2009 at 15:46 history answered Greg Muller CC BY-SA 2.5