mathematics, the coadjoint representation K {\displaystyle K} of a Lie group G {\displaystyle G} is the dual of the adjoint representation. If g {\displaystyle...
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Virasoro group (section Coadjoint representation)
viewed as a differential of the adjoint representation of the Virasoro group. Its dual, the coadjoint representation of the Virasoro group, provides the transformation...
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is the Lie subalgebra of elements of g that annihilate ξ in the coadjoint representation. The index of the Lie algebra is ind g := min ξ ∈ g ∗ dim g...
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Orbit method (category Representation theory of Lie groups)
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...
7 KB (835 words) - 17:34, 31 August 2022
Kirillov-Kostant-Souriau symplectic form of symplectic geometry, see Coadjoint representation. This disambiguation page lists articles associated with the title...
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notion of a dual canonical basis. coadjoint A coadjoint representation is the dual representation of an adjoint representation. complete “completely reducible"...
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Polarization (Lie algebra) (category Representation theory of Lie algebras)
G} act on the space g ∗ {\displaystyle {\mathfrak {g}}^{*}} via coadjoint representation A d ∗ {\displaystyle \mathrm {Ad} ^{*}} . Let O f {\displaystyle...
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that the symplectic manifold is the 2-sphere, it can be realized as a coadjoint orbit in s u ( 2 ) ∗ {\displaystyle {\mathfrak {su}}(2)^{*}} . Assuming...
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Kirillov character formula (category Representation theory of Lie groups)
orbit method gives a heuristic method in representation theory. It connects the Fourier transforms of coadjoint orbits, which lie in the dual space of the...
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worked in the construction of unitary representations of Lie groups using coadjoint orbits of the Lie algebras. She proved a generalized Poisson summation...
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g over an algebraically closed field of characteristic 0 in terms of coadjoint orbits. More precisely, it is a homeomorphism from the space of orbits...
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Nahm equations (section Lax representation)
moduli space of monopoles; and the existence of hyperkähler structure on coadjoint orbits of complex semisimple Lie groups, proved by (Kronheimer 1990),...
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introduced by Bertram Kostant (1973), states that the projection of every coadjoint orbit of a connected compact Lie group into the dual of a Cartan subalgebra...
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manifolds under any maximal compact subgroup of G, and they are precisely the coadjoint orbits of compact Lie groups. Flag manifolds can be symmetric spaces....
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Institute of Technology in 1998. Her dissertation, Admissible Nilpotent Coadjoint Orbits of p-adic Reductive Lie Groups, was supervised by David Vogan....
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structure on g ∗ {\displaystyle {\mathfrak {g}}^{*}} are the orbits of the coadjoint action of G {\displaystyle G} on g ∗ {\displaystyle {\mathfrak {g}}^{*}}...
60 KB (9,159 words) - 20:35, 28 March 2024
de Concini, Corrado; Kac, Victor G.; Procesi, Claudio (1992). "Quantum coadjoint action". Journal of the American Mathematical Society. 5 (1): 151–189...
8 KB (783 words) - 21:32, 18 August 2023