Published: 1988 Received: May 06, 1986Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: Right : [A] V. I. Arnol'd, Wave front evolution and equivariant Morse lemma, Comm. Pure Appl. Math., 29 (1976), 557-582. [Bou] N. Bourbaki, Groupes et Algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris,1968. [D1] J. Dixmier, Champs de vecteurs adjoints sur les groupes et algèbres de Lie semisimples,J. Reine Angew. Math., 309 (1979), 183-190. [D2] J. Dixmier, Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. [Ga] F. R. Gantmacher, The theory of matrices, Vol. I, Chelsea, New-York, 1960. [Gi] A. B. Givental', Displacement of invariants of groups that are generated by reflexions and are connected with simple singularities of functions, Funct. Anal. Appl., 14 (1980), 81-89. [He] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New-York, 1962. [K] B. Kostant, Lie group representations on polynomial rings, Amer. J. Math., 85 (1963), 327-404. [K-R] B. Kostant and S. Rallis, Orbits and representations associated with symmetricspaces, Amer. J. Math., 93 (1971), 753-809. [S] J. Sekiguchi, Invariant vector fields on a simple Lie algebra under the adjointaction, J. Math. Soc. Japan, 36 (1984), 147-159. [So] L. Solomon, Invariants of finite reflexion groups, Nagoya Math. J., 22 (1963), 57-64. [Sch1] G. W. Schwarz, Lifting smooth homotopies of orbit spaces, Publ. Math. IHES,51 (1980), 37-135. [Sch2] G. W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology, 14 (1975), 63-68. [Sch3] G. W. Schwarz, Representations of simple Lie groups with a free module of covariants, Invent. Math., 50 (1978),1-12. [Vu] Th. Vust, Covariants de groupes algébriques réductifs, Thèse, Univ. de Genève,1974. [Wa] N. R. Wallach, Harmonic Analysis on Homogeneous Spaces, Marcel Dekker, New-York, 1973.
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