Quantization and representation theory of finite W algebras

  title={Quantization and representation theory of finite W algebras},
  author={Jan de Boer},
In this paper we study the finitely generated algebras underlying W algebras. These so called ’finite W algebras’ are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of sl2 into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite W algebra can be embedded into the Kirillov… CONTINUE READING
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