Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian (Q845782)

The author constructs an equivariant resolution of singularities of the null-fiber of a moment map related to the dual pair \((\text{Sp}_{2n}({\mathbb R}), \text{O}_{m_1, m_2}({\mathbb R}))\) in \(\text{Sp}_{2n(m_1+m_2)}(\mathbb R)\). Conormal bundles of some closed orbits in the Lagrangian Grassmannians are realized as categorical quotients. These bundles turn out to be resolutions of singularities of the closures of some nilpotent orbits. The case of the dual pair \((\text{O}^*_{2n}, \text{Sp}_{n,n})\), \(n\) even, is discussed as well.