Dixmier Algebras for Classical Complex Nilpotent Orbits via Kraft-Procesi Models I
We attach a Dixmier algebra \(\mathcal{B}\) to the closure of \(\bar{\mathcal{O}}\) any nilpotent orbit of G where G is GL(nℂ), O(nℂ) or Sp(2n ℂ). This algebra \(\mathcal{B}\) is a noncommutative analog of the coordinate ring \(\mathcal{R} of \bar{\mathcal{O}}\) in the sense that \(\mathcal{B}\) has a G-invariant algebra filtration and \(gr\mathcal{B} = \mathcal{R}\).