Simple Weight Modules of the Lie Algebra of Vector Fields of C2
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Classification of the weight modules of the Lie algebra Wn of vector fields on C n has been a long-standing problem in the area of representation theory. In this thesis, a classification of all simple weight modules of W2 with a uniformly bounded set of weight multiplicities is provided, and much of the theory that will be needed to classify all simple weight modules of Wn with a uniformly bounded set of weight multiplicities will also be developed. To achieve this classification, a new family of generalized tensor Wn-modules is introduced, and a twisted localization functor is applied.