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Nov 15, 2009 at 13:22 vote accept Ilya Nikokoshev
Nov 15, 2009 at 2:50 comment added Ben Webster Ah, well, this is what happens when you don't explain your notation. The decomposition corresponding to weight spaces is no conjecture; any reasonable version of categorifying Kac-Moody algebras will have that property. The braid action is more interesting though. Rouquier constructs a candidate, but doesn't prove that it satisfies the braid relations.
Nov 15, 2009 at 0:53 comment added Ilya Nikokoshev According to the notes, the conjecture doesn't say that any V decomposes as a sum numbered by irreps of g, merely that V decomposes as a sum according to weights and that there's a filtration numbered by irreps. For the reference, the talk in question has notes at math.utexas.edu/users/benzvi/GRASP/lectures/IAS/…
Nov 14, 2009 at 23:45 history answered Ben Webster CC BY-SA 2.5