Orbits, Symplectic Structures and Representation Theory

Abstract

We introduce a general approach to unitary representations for all Lie groups. An underlying feature is a study of sympletic manifolds X 2n (i. e. there exists a closed non-singular 2-form on X ). If [ω] ∈ H 2 ( X, R ) is an integral class there is an associated affinely connected Hermitian line bundle L over X which is unique if X is simply connected.