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Aug 28, 2012 at 23:52 vote accept Igor Makhlin
Aug 28, 2012 at 23:32 comment added Igor Makhlin Yes, just before you posted I'd understood it was this modified concept of duality I wasn't grasping. Will have to read up on that!
Aug 28, 2012 at 23:28 comment added Jim Humphreys @Igor: Ben isn't talking about the usual dual space, but rather the BGG dual module. See my clarification and example.
Aug 28, 2012 at 23:18 comment added Igor Makhlin I'm somewhat confused. Isn't the set of weights $\Pi(V_\lambda^*)$ equal to $-\Pi(V_\lambda)$? This would stop $V_\lambda^*$ from lying in $\mathcal O$ since its set of weights would have no maximal element.
Aug 28, 2012 at 22:03 history answered Ben Webster CC BY-SA 3.0