Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft-procesi Models I
نویسنده
چکیده
We attach a Dixmier algebra B to the closure O of any nilpotent orbit of G where G is GL(n, C), O(n, C) or Sp(2n, C). This algebra B is a noncommutative analog of the coordinate ring R of O, in the sense that B has a G-invariant algebra filtration and grB = R. We obtain B by making a noncommutative analog of the Kraft-Procesi construction which modeled O as the algebraic symplectic reduction of a finite-dimensional symplectic vector space L. Indeed B is a subquotient of the Weyl algebra for L. B identifies with the quotient of U(g) by a two-sided ideal J , where g = Lie(G). Then grJ is the ideal I(O) in S(g) of functions vanishing on O. In every case where O is connected, J is a completely prime primitive ideal.
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