Coadjoint orbits of the special Euclidean group

In this report we classify the coadjoint orbits for compact semisimple Lie groups by establishing a correspondence between orbits and subsets of Dynkin diagrams. Particular attention is given to the special unitary and orthogonal groups for which the orbits are complex flags and real Hermitian flags respectively. The orbits for non-compact and nonsemisimple affine groups are discussed and in the example of the special Euclidean group a geometric bijection between adjoint and coadjoint orbits is found