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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quantization and Hamiltonian $ G$-foliations


Author: L. Pukanszky
Journal: Trans. Amer. Math. Soc. 295 (1986), 811-847
MSC: Primary 22E27; Secondary 58F06
MathSciNet review: 833711
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Abstract: As it was recognized twenty five years ago by A. A. Kirillov, in the unitary representation theory of nilpotent Lie groups a crucial role is played by orbits of the coadjoint representation. B. Kostant noted that, for any connected Lie group, these orbits admit a symplectic structure and lend themselves to an intrinsic characterization. The present author later observed, that already for the purposes of unitary representation theory of solvable Lie groups, this concept has to be enlarged and replaced by that of a generalized orbit. One objective of this paper is their intrinsic characterization. Other results prepare the way for the geometric construction of the corresponding unitary representations, to be developed later.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0833711-1
PII: S 0002-9947(1986)0833711-1
Article copyright: © Copyright 1986 American Mathematical Society