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ABSTRACT:
We summarize some properties of the groups of coherent states,
i.e. groups whose quotient with the stationary groups are manifolds
which admit a holomorphic embedding in a projective Hilbert
space. This class of groups contains all compact groups, all simple
hermitian groups, certain solvable groups and also mixed groups as the
semidirect product of the Heisenberg group and the symplectic group.
We determine the differential action of the generators of the
representation of the group of coherent states on the symmetric Fock
space attached to the Hilbert space of
the representation. This permits a realization of Lie algebras of
coherent states by first-order differential operators with holomorphic
polynomial coefficients on K\"ahler coherent state orbits.
Stefan Berceanu
"Horia Hulubei" National Institute of Physics and Nuclear
Engineering
IFIN-HH
Department of Theoretical Physics
P.O. Box MG-6, R7690
Bucharest-Magurele
Romania
E-mail: Berceanu@theor1.theory.nipne.ro
Fax: (401)-4574440
Tel. (401)-4042300/3403
http://theor1.theory.nipne.ro/m&cp/
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