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On the structure of the category O for W-algebras. (2008)cite arxiv:0812.1584 Comment: 11 pages, v2 some gaps fixed, some proofs rewritten, Remark 5.4 added, v3 15 pages, some gaps fixed, a new section is added.Finite dimensional representations of W-algebras. 0807.1023, (July 2008)Quantized symplectic actions and W-algebras. 0707.3108, (July 2007)