Dual pairs and tensor categories of modules over Lie algebras ̂ gl ∞ and W 1 + ∞
نویسنده
چکیده
We introduce a tensor category O+ (resp. O−) of certain modules of ĝl∞ with non-negative (resp. non-positive) integral central charges with the usual tensor product. We also introduce a tensor category (Of , ⊙ ) consisting of certain modules over GL(N) for all N . We show that the tensor categories O± and Of are semisimple abelian and all equivalent to each other. We give a formula to decompose a tensor product of two modules in each of these categories. We also introduce a tensor category O of certain modules over W1+∞ with non-negative integral central charges. We show that O is semisimple abelian and give an explicit formula to decompose a tensor product of two modules in O.
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