Skip to main content
SpringerLink
Log in

Convexity and unitary representations of nilpotent Lie groups

  • Published:
Inventiones mathematicae Aims and scope

Summary

The moment map of symplectic geometry is extended to associate to any unitary representation of a nilpotent Lie group aG-invariant subset of the dual of the Lie algebra. We prove that this subset is the closed conex hull of the Kirillov orbit of the representation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Bibliography

  1. Arnal, D., Cortet, J.C. [1]: Nilpotent Fourier transform and applications. Lett. Math. Phys.9, 25–34 (1985)

    Google Scholar 

  2. Atiyah, M.F. [1]: Convexity and commuting Hamiltonians. Bull. Lond. Math. Soc.14, 1–15 (1982)

    Google Scholar 

  3. Atiyah, M.F. [2]: Angular Momentum, Convex polyhedra and Algebraic Geometry. Proc. Edinburgh Math. Soc.26, 121–138 (1983)

    Google Scholar 

  4. Grünbaum, B. [1]: Convex Polytopes. New York: John Wiley and Sons 1967

    Google Scholar 

  5. Guillemin, V., Sternberg, S. [1]: Convexity Properties of the moment mapping. Invent. Math.67, 491–513 (1982)

    Google Scholar 

  6. Guillemin, V., Sternberg, S. [2]: Convexity Properties of the moment mapping, II. Invent. Math.77, 533–546 (1984)

    Google Scholar 

  7. Howe, R. [1]: Quantum mechanics and partial differential equations. J. Funct. Anal.38, 188–254 (1980)

    Google Scholar 

  8. Kirillov, A.A. [1]: Representations of Nilpotent Lie Groups. Russian Math. Surveys17, 53–103 (1962)

    Google Scholar 

  9. Kirwan, F. [1]: Convexity Properties of the moment mapping, III. Invent. Math.77, 547–552 (1984)

    Google Scholar 

  10. Kostant, B. [1]: Quantization and Unitary Representations. Lect. Notes Math. vol. 170, Berlin Heidelberg New York: Springer, 1970, pp. 87–208

    Google Scholar 

  11. Souriau, J.M. [1]: Structure des systèmes dynamiques. Paris: Dunod, 1970

    Google Scholar 

  12. Wildberger, N.J. [1]: Quantization and Harmonic Analysis on Nilpotent Lie groups. Thesis, Yale University 1983

  13. Wildberger, N.J. [2]: The moment map of a Lie group representation (preprint)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Ontario, Canada

    N. J. Wildberger

Authors
  1. N. J. Wildberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by NSERC research grant no. A7918

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wildberger, N.J. Convexity and unitary representations of nilpotent Lie groups. Invent Math 98, 281–292 (1989). https://doi.org/10.1007/BF01388854

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388854

Keywords

Search

Navigation