Quantized symplectic actions and W-algebras

Details Quantized symplectic actions and W-algebras Quantized symplectic actions and W-algebras

2007-07-20

arxiv.org/abs/0707.3108v5

J. Amer. Math. Soc. 23(2010), 35-59

Mathematics

Representation Theory

v1 21 pages, v2 Hamiltonian actions are no longer used whence the change of title. Proofs of Theorem 1.2.2(iii),(vi) and Theor

Scientific paper

With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian reduction. We observe that W is the invariant algebra for an action of a reductive group G with Lie algebra g on a quantized symplectic affine variety and use this observation to study W. Our results include an alternative definition of W, a relation between the sets of prime ideals of W and of the corresponding universal enveloping algebra, the existence of a one-dimensional representation of W in the case of classical g and the separation of elements of W by finite dimensional representations.

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