Quantization and Hamiltonian $G$-foliations
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- by L. Pukanszky PDF
- Trans. Amer. Math. Soc. 295 (1986), 811-847 Request permission
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.References
- L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255–354. MR 293012, DOI 10.1007/BF01389744
- Raoul Bott and Loring W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics, vol. 82, Springer-Verlag, New York-Berlin, 1982. MR 658304, DOI 10.1007/978-1-4757-3951-0
- Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 87–208. MR 0294568
- L. Pukanszky, Action of algebraic groups of automorphisms on the dual of a class of type $\textrm {I}$ groups, Ann. Sci. École Norm. Sup. (4) 5 (1972), 379–395. MR 322102, DOI 10.24033/asens.1231
- L. Pukanszky, Unitary representations of solvable Lie groups, Ann. Sci. École Norm. Sup. (4) 4 (1971), 457–608. MR 439985, DOI 10.24033/asens.1218
- L. Pukanszky, The primitive ideal space of solvable Lie groups, Invent. Math. 22 (1973), 75–118. MR 333078, DOI 10.1007/BF01392298
- L. Pukanszky, Characters of connected Lie groups, Acta Math. 133 (1974), 81–137. MR 409728, DOI 10.1007/BF02392143
- L. Pukanszky, Unitary representation of Lie groups and generalized symplectic geometry, Operator algebras and applications, Part 1 (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, RI, 1982, pp. 435–466. MR 679726
- L. Pukanszky, Symplectic structure on generalized orbits of solvable Lie groups, J. Reine Angew. Math. 347 (1984), 33–68. MR 733046, DOI 10.1515/crll.1984.347.33
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 295 (1986), 811-847
- MSC: Primary 22E27; Secondary 58F06
- DOI: https://doi.org/10.1090/S0002-9947-1986-0833711-1
- MathSciNet review: 833711