Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The Mackey obstruction and the coadjoint orbits


Author: Zongyi Li
Journal: Trans. Amer. Math. Soc. 346 (1994), 693-705
MSC: Primary 22E60; Secondary 22E25, 58F06
MathSciNet review: 1276935
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper studies the Mackey obstruction representation theory at the coadjoint orbit level. It shows how to get rid of such obstructions and to get orbits of the "little groups". Such little group data is essential for inductive construction of coadjoint orbits of general Lie groups.


References [Enhancements On Off] (What's this?)

  • [1] L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255–354. MR 0293012
  • [2] Jonathan Brezin, Unitary representation theory for solvable Lie groups, Memoirs of the American Mathematical Society, No. 79, American Mathematical Society, Providence, R.I., 1968. MR 0227311
  • [3] Robert L. Bryant, An introduction to Lie groups and symplectic geometry, Geometry and quantum field theory (Park City, UT, 1991) IAS/Park City Math. Ser., vol. 1, Amer. Math. Soc., Providence, RI, 1995, pp. 5–181. MR 1338391
  • [4] Victor Guillemin and Shlomo Sternberg, Symplectic techniques in physics, Cambridge University Press, Cambridge, 1984. MR 770935
  • [5] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57–110 (Russian). MR 0142001
  • [6] Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, pp. 87–208. Lecture Notes in Math., Vol. 170. MR 0294568
  • [7] Z. Li, Coadjoint orbits and induced representations, Ph.D. Thesis, MIT, 1993.
  • [8] George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 0044536
  • [9] George W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265–311. MR 0098328
  • [10] George W. Mackey, The theory of unitary group representations, University of Chicago Press, Chicago, Ill.-London, 1976. Based on notes by James M. G. Fell and David B. Lowdenslager of lectures given at the University of Chicago, Chicago, Ill., 1955; Chicago Lectures in Mathematics. MR 0396826

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E60, 22E25, 58F06

Retrieve articles in all journals with MSC: 22E60, 22E25, 58F06


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1276935-9
Keywords: Coadjoint orbit, the Mackey obstruction, symplectic manifold, Hamiltonian action, moment map
Article copyright: © Copyright 1994 American Mathematical Society