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Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft-Procesi Models I

Ranee Brylinski
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Abstract

We attach a Dixmier algebra B to the closure 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 the orbit closure, in the sense that B has a G-invariant algebra filtration and gr B=R. We obtain B by making a noncommutative analog of the Kraft-Procesi construction which modeled the orbit closure as the algebraic symplectic reduction of a finite-dimensional symplectic vector space L. Indeed B is a subquotient of the Weyl algebra for L.

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BibTeXRIS

Ranee Brylinski. 2003-03-27. Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft-Procesi Models I. https://arxiv.org/abs/math/0201103

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