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Kirillov 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 Group action (mathematics), action of the group on the dual space of its Lie algebra. The theory was introduced by for nilpotent groups and later extended by Bertram Kostant, Louis Auslander, Lajos Pukánszky and others to the case of solvable groups. Roger Evans Howe, 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. Relation with symplectic geometry One of the key observations of Kirillov was that coadjoint orbits of a Lie group ''G'' have natural structure of symplectic manifolds whose symplectic structure is invariant under ''G''. If an orbi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
