Kirillov orbit theory
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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 
. 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 . The theory was developed by Alexandre Kirillov originally for nilpotent groups and further by Bertram Kostant, Louis Auslander and others for solvable groups.
[edit] See also
[edit] Reference
- A. Kirillov, Éléments de la Théorie des Représentations, (French translation) Éditions MIR, Moscow, 1974
