CONSTRUCTION OF HOMOGENEOUS LAGRANGIAN SUBMANIFOLDS IN $\boldsymbol{CP}^N$ AND HAMILTONIAN STABILITY

Abstract

We apply the concept of castling transform of prehomogeneous vector spaces to produce new examples of minimal homogeneous Lagrangian submanifolds in the complex projective space. Furthermore we verify the Hamiltonian stability of a low dimensional example that can be obtained in this way.