English

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

Representation Theory 2007-05-23 v2 Quantum Algebra

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.

Keywords

Cite

@article{arxiv.math/0201103,
  title  = {Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft-Procesi Models I},
  author = {Ranee Brylinski},
  journal= {arXiv preprint arXiv:math/0201103},
  year   = {2007}
}

Comments

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-mail

R2 v1 2026-07-22T16:42:39.647Z