Quantized symplectic actions and W-algebras
Lie Theory
March 13, 2008 09:30 AM to 10:30 AM
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Abstract: |
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. The study of W-algebras
traces back to the
celebrated Kostant paper "On Whittaker vectors and representation
theory", 1978. 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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Lecture #12681
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