Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

Abstract

We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed K C -orbits in the Lagrangian Grassmannian as categorical quotients. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent K C -orbits, which is a "quotient" of the resolution of the null fiber. Mathematics Subject Classification (2000)Primary 14M15 · 14E15 · Secondary 14L30 · 22E47 · 20G05