Advertisement

Inventiones mathematicae

, Volume 49, Issue 2, pp 167–191 | Cite as

Representations of simple lie groups with regular rings of invariants

  • Gerald W. Schwarz
Article

Keywords

Regular Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 2.
    Bourbaki, N.: Groupes et Algèbres de Lie. Paris: Hermann 1968Google Scholar
  3. 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 1973Google Scholar
  4. 4.
    Chevalley, C.: Invariants of finite groups generated by reflections. Amer. J. Math.77, 778–782 (1955)Google Scholar
  5. 5.
    Dynkin, E.B.: Semisimple subalgebras of semisimple Lie algebras. Amer. Math. Soc. Transl.6, 111–244 (1957)Google Scholar
  6. 6.
    Dynkin, E.B.: Maximal subgroups of the classical groups. Amer. Math. Soc. Transl.6, 245–378 (1957)Google Scholar
  7. 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. 8.
    Gurevich, G.B.: Foundations of the Theory of Algebraic Invariants. Groningen: Noordhoff 1964Google Scholar
  9. 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. 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. 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. 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. 13.
    Kostant, B.: Lie group representations on polynomial rings. Amer. J. Math.85, 327–402 (1963)Google Scholar
  14. 14.
    Kostant, B., Rallis, S.: On representations associated with symmetric spaces. Bull. Amer. Math. Soc.75, 884–888 (1969)Google Scholar
  15. 15.
    Krämer, M.: Eine Klassifikation bestimmter Untergruppen kompakter zusammenhängender Liegruppen. Comm. in Alg.3, 691–737 (1975)Google Scholar
  16. 16.
    Krämer, M.: Über Untergruppen kompakter Liegruppen als Isotropiegruppen bei linearen Aktionen. Math. Z.147, 207–224 (1976)Google Scholar
  17. 17.
    Krämer, M.: Some tips on the decomposition of tensor product representations of compact connected Lie groups. To appear in Reports an Mathematical Physics.Google Scholar
  18. 18.
    Luna, D.: Slices étales. Bull. Soc. Math. France, Mémoire33, 81–105 (1973)Google Scholar
  19. 19.
    Luna, D.: Adhérences d'orbite et invariants. Invent. Math.29, 231–238 (1975)Google Scholar
  20. 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. 21.
    Mumford, D.: Geometric Invariant Theory, Erg. der Math. Bd. 34, New York: Springer-Verlag 1965Google Scholar
  22. 22.
    Mumford, D.: Introduction to Algebraic Geometry, preliminary version. Cambridge: Harvard University 1966Google Scholar
  23. 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. 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. 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. 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. 27.
    Popov, V.L.: Representations with a free module of covariants. Functional Anal. Appl.10, 242–244 (1977)Google Scholar
  28. 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 1972Google Scholar
  29. 29.
    Schwarz, G.W.: Lifting smooth homotopies of orbit spaces. To appear in Inst. Hautes Études Sci. Publ. Math.Google Scholar
  30. 30.
    Vinberg, É.B.: The Weyl group of a graded Lie algebra, Math. USSR-Izvestija10, 463–495 (1976)Google Scholar
  31. 31.
    Wallach, N.: Minimal immersions of symmetric spaces into spheres. In: Symmetric Spaces, pp. 1–40. New York: Marcel Dekker 1972Google Scholar
  32. 32.
    Weyl, H.: The Classical Groups, 2nd edn., Princeton: Princeton University Press 1946Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Gerald W. Schwarz
    • 1
  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA

Personalised recommendations