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)

 
 

 

Théorie de Sullivan pour la cohomologie à coefficients locaux


Author: Antonio Gómez-Tato
Journal: Trans. Amer. Math. Soc. 330 (1992), 235-305
MSC: Primary 55P62; Secondary 57R99, 58A99
DOI: https://doi.org/10.1090/S0002-9947-1992-1028765-9
MathSciNet review: 1028765
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The classical moment map of symplectic geometry is used to canonically associate to a unitary representation of a Lie group $ G$ a $ G$-invariant subset of the dual of the Lie algebra. This correspondence is in some sense dual to geometric quantization. The nature and convexity of this subset is investigated for $ G$ compact semisimple.


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

  • [1] V. I. Arnold, Mathematical methods of classical mechanics, Springer-Verlag, Berlin, 1980. MR 997295 (90c:58046)
  • [2] M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15. MR 642416 (83e:53037)
  • [3] -, Angular momentum, convex polyhedra and algebraic geometry, Proc. Edinburgh Math. Soc. 26 (1983), 121-138. MR 705256 (85a:58027)
  • [4] V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), 491-513. MR 664117 (83m:58037)
  • [5] -, Convexity properties of the moment mapping, II, Invent. Math. 77 (1984), 533-546. MR 759258 (86b:58042a)
  • [6] S. Helgason, Groups and geometric analysis, Academic Press, Orlando, Fla., 1984. MR 754767 (86c:22017)
  • [7] A. A. Kirillov, Representations of nilpotent Lie groups, Russian Math. Surveys 17, No. 4 (1962), 53-103. MR 0142001 (25:5396)
  • [8] F. Kirwan, Convexity properties of the moment mapping, III, Invent. Math. 77 (1984), 547-552. MR 759257 (86b:58042b)
  • [9] B. Kostant, Quantization and unitary representations, Lecture Notes in Math., vol. 170, Springer-Verlag, Berlin, 1970, pp. 87-208. MR 0294568 (45:3638)
  • [10] -, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. 6 (1973), 413-455. MR 0364552 (51:806)
  • [11] J. M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970. MR 0260238 (41:4866)
  • [12] N. J. Wildberger, Convexity and representations of nilpotent Lie groups, Invent. Math. 98 (1989), 281-292. MR 1016265 (90j:22007)
  • [13] N. J. Wildberger, On the Fourier transform of a compact semisimple Lie group, (preprint). MR 1250994 (95g:22026)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55P62, 57R99, 58A99

Retrieve articles in all journals with MSC: 55P62, 57R99, 58A99


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1028765-9
Keywords: Moment map, unitary representations, coadjoint orbits, convexity
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society