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Feb 23, 2011 at 16:46 comment added S. Carnahan Minor correction: The categories in number 2 are made out of projective $\mathfrak{g}((t))$-modules at the critical level. By "critical level", one means the central line of the central extension acts in a way that gives a completion of the enveloping algebra a very large center (isomorphic to the coordinate ring of a space of opers).
Feb 23, 2011 at 13:59 history answered S. Carnahan CC BY-SA 2.5