Representation theory of Lie groups

Orbit method

In mathematics, the orbit method (also known as the Kirillov theory, the method of coadjoint orbits and by a few similar names) establishes a correspondence between irreducible unitary representations of a Lie group and its coadjoint orbits: orbits of the action of the group on the dual space of its Lie algebra. The theory was introduced by Kirillov for nilpotent groups and later extended by Bertram Kostant, Louis Auslander, Lajos Pukánszky and others to the case of solvable groups. Roger Howe found a version of the orbit method that applies to p-adic Lie groups.David Vogan proposed that the orbit method should serve as a unifying principle in the description of the unitary duals of real reductive Lie groups. (Wikipedia).

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Related pages

Support (mathematics) | Lie group | Jacobian matrix and determinant | Geometric quantization | Fourier transform | Hamiltonian mechanics | Exponential map (Lie theory) | Polarization (Lie algebra) | Harish-Chandra character | Nilpotent | Phase space | Infinitesimal character | Representation theory | Connected space | Kirillov character formula | Dirac delta function | Dual space | Mathematics | Nilpotent group | Cartan subalgebra | Lie algebra | Compact group | Dixmier mapping | Solvable group | Symplectic manifold | Unitary representation | Irreducible representation | Closed set