Localization of U-modules. Iv. Localization on P
نویسندگان
چکیده
This result is strikingly similar to the following hoped-for picture of affine Lie algebra representation theory, explained to us by A.Beilinson. Let M1,M2 be two modules over an affine Lie algebra ĝ on the critical level. One hopes that there is a localization functor which associates to these modules perverse sheaves ∆(M1),∆(M2) over the semiinfinite flag space Ĝ/B̂. Suppose that ∆(M1) and ∆(M2) are equivariant with respect to the opposite Borel subgroups of Ĝ. Then the intersection S of their supports is finite dimensional, and one hopes that RΓ(S,∆(M1)⊗∆(M2)) = Tor∞ 2 −•(M1,M2)
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