Orbit method

The Kirillov orbit theory or the method of orbits is a parametrization of the unitary equivalence classes of irreducible representations of a connected nilpotent Lie group G by the orbits of the action G on the dual of its Lie algebra ${\mathfrak {g}}^{*}$. These orbits are also called coadjoint orbits. The theory was developed by A. Kirillov.

Reference

• A. Kirillov, Éléments de la Théorie des Représentations, (French translation) Éditions MIR, Moscow, 1974