Inventiones mathematicae

, Volume 50, Issue 1, pp 1–12

Representations of simple Lie groups with a free module of covariants

  • Gerald W. Schwarz


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bourbaki, N.: Algèbre, 3rd edn., Paris: Hermann, 1962Google Scholar
  2. 2.
    Dieudonné, J., Carrell, J.: Invariant theory, old and new. Adv. in Math.4, 1–80 (1970)Google Scholar
  3. 3.
    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
  4. 4.
    Grothendieck, A.: Cohomologie Locale des Faisceaux et Théorèmes de Lefschetz Locaux et Globaux (SGA 2), Amsterdam: North Holland, 1968Google Scholar
  5. 5.
    Gurevich, G.B.: Foundations of the Theory of Algebraic Invariants, Groningen: Noordhoff, 1964Google Scholar
  6. 6.
    Hsiang, W.C., Hsiang, W.Y.: Differentiable actions of compact connected classical groups: II. Ann. of Math.92, 189–223 (1970)Google Scholar
  7. 7.
    Igusa, J.-I.: Geometry of absolutely admissible representations. In: Number Theory, Algebraic Geometry and Commutative Algebra, pp. 373–452. Tokyo: Kinokuniya, 1973Google Scholar
  8. 8.
    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
  9. 9.
    Kostant, B.: Lie group representations on polynomial rings. Amer. J. Math.85, 327–402 (1963)Google Scholar
  10. 10.
    Luna, D.: Slices étales. Bull. Soc. Math. France, Mémoire33, 81–105 (1973)Google Scholar
  11. 11.
    Luna, D.: Adhérences d'orbite et invariants, Invent. Math.29, 231–238 (1975)Google Scholar
  12. 12.
    Mumford, D.: Geometric Invariant Theory, Erg. der Math. Bd. 34, New York: Springer-Verlag 1965Google Scholar
  13. 13.
    Popov, A.M.: Irreducible simple linear Lie groups with finite standard subgroups of general position. Functional Anal. Appl.9, 346–347 (1976)Google Scholar
  14. 14.
    Popov, V.L.: Representations with a free module of covariants. Functional Anal. Appl.10, 242–244 (1977)Google Scholar
  15. 15.
    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
  16. 16.
    Schwarz, G.W.: Lifting smooth homotopies of orbit spaces. To appear in Inst. Hautes Études Sci. Publ. Math.Google Scholar
  17. 17.
    Schwarz, G.W.: Representations of simple Lie groups with regular rings of invariants. Inv. Math.49, 167–191 (1978)Google Scholar
  18. 18.
    Serre, J.-P.: Algèbre Locale-Multiplicités, Lecture Notes in Mathematics No. 11, New York: Springer-Verlag, 1965Google Scholar
  19. 19.
    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