Classification of Lagrangian stars and their symplectic reductions

Abstract

The Lagrangian star is a germ of the system of Lagrangian submanifolds in the symplectic manifold . We investigate the symplectic group action on Lagrangian stars and construct the basic invariants of such action. The Kashiwara signature for 3-Lagrangian linear stars is generalized to the nonlinear case and the generalized contact classes for Lagrangian stars are constructed. Finally, we obtain the generic classification of simple normal forms of reduced Lagrangian stars with respect to a hypersurface.