Skip to main content
SpringerLink
Log in

Inequalities defining orbit spaces

  • Published:
Inventiones mathematicae Aims and scope

Summary

The orbit space of a representation of a compact Lie group has a natural semialgebraic structure. We describe explicit ways of finding the inequalities defining this structure, and we give some applications.

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

References

  1. Abud, M., Sartori, G.: The geometry of orbit-space and natural minima of Higgs potentials. Phys. Lett.104, 147–152 (1981)

    Google Scholar 

  2. Abud, M., Sartori, G.: The geometry of spontaneous symmetry breaking. Ann. Phys.150, 307–370 (1983)

    Google Scholar 

  3. Bierstone, E.: Lifting isotopies from orbit spaces. Topology14, 245–252 (1975)

    Google Scholar 

  4. Birkes, D.: Orbits of linear algebraic groups. Ann. Math.93, 459–475 (1971)

    Google Scholar 

  5. Bochnak, J., Efroymson, G.: Real algebraic geometry and the 17th Hilbert problem. Math. Ann.251, 213–241 (1980)

    Google Scholar 

  6. Chevalley, C.: Theory of Lie Groups. Princeton: Princeton University Press 1946

    Google Scholar 

  7. Dadok, J., Kac, V.: Polar representations. J. Algebra (To appear)

  8. Demazure, M., Gabriel, P.: Groupes Algébriques. Amsterdam: North Holland 1970

    Google Scholar 

  9. Gatto, R., Sartori, G.: Gauge symmetry in supersymmetric gauge theories: Necessary and sufficient condition. Phys. Lett.118, 79–84 (1982)

    Google Scholar 

  10. Helgason, S.: Differential Geometry, Lie Groups and Symmetric Spaces. New York: Academic Press 1978

    Google Scholar 

  11. Kempf, G., Ness, L.: The length of vectors in representation spaces. In: Algebraic Geometry. Lect. Notes Math.732, 233–243. New York: Springer 1979

    Google Scholar 

  12. Luna, D.: Slices étales. Bull. Soc. Math. Fr. Mém.33, 81–105 (1973)

    Google Scholar 

  13. Luna, D.: Sur certains opérations différentiables des groupes de Lie. Am. J. Math.97, 172–181 (1975)

    Google Scholar 

  14. Procesi, C.: Positive symmetric functions. Adv. Math.29, 219–225 (1978)

    Google Scholar 

  15. Sartori, G.: A theorem on orbit structures (strata) of compact linear Lie groups. J. Math. Phys.24, 765–768 (1983)

    Google Scholar 

  16. Schwarz, G.: Smooth functions invariant under the action of a compact Lie group. Topology14, 63–68 (1975)

    Google Scholar 

  17. Schwarz, G.: Lifting smooth homotopies of orbit spaces. Publ. Math. IHES51, 37–136 (1980)

    Google Scholar 

  18. Weyl, H.: The Classical Groups, 2nd ed. Princeton: Princeton University Press 1946

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Istituto “Guido Castelnuovo”, Università degli Studi di Roma, I-00185, Roma, Italy

    Claudio Procesi

  2. Department of Mathematics, Brandeis University, 02254, Waltham, MA, USA

    Gerald Schwarz

Authors
  1. Claudio Procesi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerald Schwarz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by National Science Foundation Grant #MCS 8302575

Rights and permissions

Reprints and permissions

About this article

Cite this article

Procesi, C., Schwarz, G. Inequalities defining orbit spaces. Invent Math 81, 539–554 (1985). https://doi.org/10.1007/BF01388587

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388587

Keywords

Search

Navigation