Kirillov orbit theory

The Kirillov orbit theory or the method of orbits establishes a correspondence between the set of unitary equivalence classes of irreducible representations of a Lie group and the orbits of the action of "G" on the dual of its Lie algebra $mathfrak\{g\}^*$. These orbits are also called coadjoint orbits.

For example if "G" is a connected, simply connected nilpotent Lie group , the equivalence classes of irreducible unitary representations of "G" are parametrized by the orbits of the action "G" on $mathfrak\{g\}^*$. The theory was developed by Alexandre Kirillov originally for nilpotent groups and further by Bertram Kostant, Louis Auslander and others for solvable groups.

ee also

*Kirillov character formula

References

* (French translation)
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