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This is great. I didn't know the total space of the GCSGL degeneration was not smooth. What do you know about going in the other direction? i.e. stealing a toric degeneration from an integrable system.
What I said is not quite right. It can happen (and does happen here) that FG is exact while F is only left exact. The question I should have asked is: are the modules (R^i Ind_P^G)(Res_L^P M) independent of P?
Parabolic induction has right-derived functors, because Ind_P^G does. Are these also independent of P? Also, can you say more about the Mackey formula argument?
Is it special to three dimensions that the four-manifold it bounds only needs to by almost complex? It makes it sound like a CR structure is just an almost complex structure on M x R.
