Infinitesimally tight Lagrangian orbits (Q2663109)

This paper is devoted to the following problem: Let \((M, \omega)\) be a connected symplectic manifold, \(G\) a Lie group with Lie algebra \(g\), and \(L\) a Lie subgroup of \(G\); assume that \(G\) acts on \(M\) such that the action is Hamiltonian and admits a moment map \(\mu : M \longrightarrow G^*\) which is \(\operatorname{Ad}^*\)-equivariant. The question is to identify those orbits \(Lx\) with \(x \in M\) that are Lagrangian submanifolds of \((M, \omega)\), or more generally, isotropic submanifolds. The authors discuss the intersection theory for such Lagrangian submanifolds, and introduce the notion of infinitesimally tight. The paper also contains two interesting appendices: In Appendix A the KKS (Katzarkov-Kontsevich-Pantev) symplectic form on adjoint orbits of orthogonal Lie Groups is described; and in Appendix B the authors give a list of open problems about Lagrangian orbits.