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Jul 24, 2010 at 15:44 comment added Jim Humphreys It's probably helpful to add a reference, though people studying infinite dimensional representations of reductive groups in characteristic 0 tend to focus on Lie groups. So I'm not sure what a "standard" reference would be, though Hochschild's books get into the interface with algebraic groups. Even though Jantzen's book Representations of Algebraic Groups is aimed mainly at prime characteristic, much of the foundational material he covers at first is in the spirit of this question.
Jul 20, 2010 at 6:40 vote accept Oren Ben-Bassat
Jul 19, 2010 at 22:41 history answered BCnrd CC BY-SA 2.5