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 \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.

[edit] See also

[edit] References

  • A. Kirillov, Éléments de la Théorie des Représentations, (French translation) Éditions MIR, Moscow, 1974
  • Kirillov, A. A., Lectures on the orbit method. Graduate Studies in Mathematics, 64. American Mathematical Society, Providence, RI, 2004. xx+408 pp. ISBN 0-8218-3530-0
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