Skip to main content
SpringerLink
Log in

Representations of simple lie groups with regular rings of invariants

  • Published:
Inventiones mathematicae Aims and scope

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

References

  1. Andreev, E.M., Vinberg, É.B., Élashvili, A.G.: Orbits of greatest dimension in semi-simple linear Lie groups. Functional Anal. Appl.1, 257–261 (1967)

    Google Scholar 

  2. Bourbaki, N.: Groupes et Algèbres de Lie. Paris: Hermann 1968

    Google Scholar 

  3. Chéniot, D., Lê Dũng Tráng: Remarques sur les deux exposés précédents. In: Singularités à Cargèse, Astérisque7–8, pp. 253–261. Paris: Société Mathématique de France 1973

    Google Scholar 

  4. Chevalley, C.: Invariants of finite groups generated by reflections. Amer. J. Math.77, 778–782 (1955)

    Google Scholar 

  5. Dynkin, E.B.: Semisimple subalgebras of semisimple Lie algebras. Amer. Math. Soc. Transl.6, 111–244 (1957)

    Google Scholar 

  6. Dynkin, E.B.: Maximal subgroups of the classical groups. Amer. Math. Soc. Transl.6, 245–378 (1957)

    Google Scholar 

  7. Élashvili, A.G.: Canonical form and stationary subalgebras of points of general position for simple linear Lie groups. Functional Anal. Appl.6, 44–53 (1972)

    Google Scholar 

  8. Gurevich, G.B.: Foundations of the Theory of Algebraic Invariants. Groningen: Noordhoff 1964

    Google Scholar 

  9. Hamm, H.A., Lê Dũng Tráng: Un théorème de Zariski du type de Lefschetz. Ann. Sci. École Norm. Sup.6, 317–366 (1973)

    Google Scholar 

  10. Hsiang, W.C., Hsiang, W.Y.: Differentiable actions of compact connected classical groups: II. Ann. of Math.92, 189–223 (1970)

    Google Scholar 

  11. Kac, V.G.: Concerning the question of describing the orbit space of a linear algebraic group. Usp. Matem. Nauk30, 173–174 (1975)

    Google Scholar 

  12. Kac, V.G., Popov, V.L., Vinberg, É.B.: Sur les groupes linéaires algébriques dont l'algèbre des invariants est libre. C. R. Acad. Sci. Paris283, 875–878 (1976)

    Google Scholar 

  13. Kostant, B.: Lie group representations on polynomial rings. Amer. J. Math.85, 327–402 (1963)

    Google Scholar 

  14. Kostant, B., Rallis, S.: On representations associated with symmetric spaces. Bull. Amer. Math. Soc.75, 884–888 (1969)

    Google Scholar 

  15. Krämer, M.: Eine Klassifikation bestimmter Untergruppen kompakter zusammenhängender Liegruppen. Comm. in Alg.3, 691–737 (1975)

    Google Scholar 

  16. Krämer, M.: Über Untergruppen kompakter Liegruppen als Isotropiegruppen bei linearen Aktionen. Math. Z.147, 207–224 (1976)

    Google Scholar 

  17. Krämer, M.: Some tips on the decomposition of tensor product representations of compact connected Lie groups. To appear in Reports an Mathematical Physics.

  18. Luna, D.: Slices étales. Bull. Soc. Math. France, Mémoire33, 81–105 (1973)

    Google Scholar 

  19. Luna, D.: Adhérences d'orbite et invariants. Invent. Math.29, 231–238 (1975)

    Google Scholar 

  20. Luna, D., Vust, T.: Un théorème sur les orbites affines des groupes algébriques semi-simples. Ann. Scuola Norm. Sup. Pisa27, 527–535 (1973)

    Google Scholar 

  21. Mumford, D.: Geometric Invariant Theory, Erg. der Math. Bd. 34, New York: Springer-Verlag 1965

    Google Scholar 

  22. Mumford, D.: Introduction to Algebraic Geometry, preliminary version. Cambridge: Harvard University 1966

    Google Scholar 

  23. Popov, A.M.: Irreducible simple linear Lie groups with finite standard subgroups of general position. Functional Anal. Appl.9, 346–347 (1976)

    Google Scholar 

  24. Popov, A.M.: Stationary subgroups of general position for certain actions of simple Lie groups. Functional Anal. Appl.10, 239–241 (1977)

    Google Scholar 

  25. Popov, V.L.: Stability criteria for the action of a semi-simple group on a factorial manifold. Math. USSR-Izvestija4, 527–535 (1970)

    Google Scholar 

  26. Popov, V.L.: The classification of representations which are exceptional in the sense of Igusa. Functional Anal. Appl.9, 348–350 (1976)

    Google Scholar 

  27. Popov, V.L.: Representations with a free module of covariants. Functional Anal. Appl.10, 242–244 (1977)

    Google Scholar 

  28. Rallis, S.: New and old results in invariant theory with applications to arithmetic groups. In: Symmetric Spaces, pp. 443–458. New York: Marcel Dekker 1972

    Google Scholar 

  29. Schwarz, G.W.: Lifting smooth homotopies of orbit spaces. To appear in Inst. Hautes Études Sci. Publ. Math.

  30. Vinberg, É.B.: The Weyl group of a graded Lie algebra, Math. USSR-Izvestija10, 463–495 (1976)

    Google Scholar 

  31. Wallach, N.: Minimal immersions of symmetric spaces into spheres. In: Symmetric Spaces, pp. 1–40. New York: Marcel Dekker 1972

    Google Scholar 

  32. Weyl, H.: The Classical Groups, 2nd edn., Princeton: Princeton University Press 1946

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Brandeis University, 02154, Waltham, Massachusetts, USA

    Gerald W. Schwarz

Authors
  1. Gerald W. Schwarz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by NSF grant MCS 77-04522. AMS (MOS) subject classifications 1970. Primary 15A72, 20G05

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schwarz, G.W. Representations of simple lie groups with regular rings of invariants. Invent Math 49, 167–191 (1978). https://doi.org/10.1007/BF01403085

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01403085

Keywords

Search

Navigation