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

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

2002-01-11

arxiv.org/abs/math/0201103v2

Mathematics

Representation Theory

16 pages. I added a half page of exposition and corrected some typos. Look at the end for my new addresses for hard mail and e

Scientific paper

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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