## Coisotropic bundles and induced representations.(English)Zbl 0568.58017

This paper deals with the concept of ”symplectic induction” introduced by A. Weinstein [Lett. Math. Phys. 2, 417-420 (1978; Zbl 0388.58010)]. This procedure starts from a Lie group G and a Lie subgroup H and associates to each Hamiltonian H-space some Hamiltonian G-space, which carries the structure of a coisotropic bundle over G/H. (A coisotropic bundle is a symplectic manifold which is fibered into coisotropic submanifolds.) In the present paper complex symplectic geometry is used in order to replace real coisotropic bundles by complex Lagrangian bundles. Especially the case where the base manifold G/H is a flag manifold is considered. Some new theorems are presented without proof. (The author announces a more detailed paper containing all proofs.)
Reviewer: V.Perlick

### MSC:

 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 53D50 Geometric quantization

Zbl 0388.58010