Lisiecki, Wojciech Coisotropic bundles and induced representations. (English) Zbl 0568.58017 Suppl. Rend. Circ. Mat. Palermo, II. Ser. 6, 201-214 (1984). 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 Keywords:homogeneous space; symplectic induction; coisotropic bundle; complex symplectic geometry; flag manifold Citations:Zbl 0388.58010 PDFBibTeX XMLCite \textit{W. Lisiecki}, Suppl. Rend. Circ. Mat. Palermo (2) 6, 201--214 (1984; Zbl 0568.58017)