Real analytic actions of complex symplectic groups and other classical Lie groups on spheres

Fuichi UCHIDA

doi:10.2969/jmsj/03840661

Fuichi UCHIDA

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 4 Pages 661-677

DOI https://doi.org/10.2969/jmsj/03840661

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Published: 1986 Received: April 09, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) C. Chevalley, Theory of Lie groups I, Princeton Univ. Press, 1946.
2) H. Grauert, On Levi's problem and the imbedding of real analytic manifolds, Ann. of Math., 68 (1958), 460-472.
3) V. W. Guillemin and S. Sternberg, Remarks on a paper of Hermann, Trans. Amer. Math. Soc., 130 (1968), 110-116.
4) W. C. Hsiang and W. Y. Hsiang, Differentiable actions of compact connected classical groups I, Amer. J. Math., 89 (1967), 705-786.
5) A. Nakanishi and F. Uchida, Actions of symplectic groups on certain manifolds, Tohoku Math. J., 36 (1984), 81-98.
6) R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc., 22, 1957.
7) F. Uchida, Real analytic SL(n, R) actions on spheres, Tohoku Math. J., 33 (1981), 145-175.
8) F. Uchida, Real analytic SL(n, C) actions, Bull. Yamagata Univ. Nat. Sci., 10 (1980), 1-14.
9) F. Uchida, Actions of special linear groups on a product manifold, Bull. Yamagata Univ. Nat. Sci., 10 (1982), 227-233.
10) F. Uchida, On the non-existence of smooth actions of complex symplectic group on cohomology quaternion projective spaces, Hokkaido Math. J., 12 (1983), 226-236.
11) T. Wada, Smooth Sp(n) actions on cohomology quaternion projective spaces, Tohoku Math. J., 29 (1977), 375-384.
12) H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., 36 (1934), 63-89.

Right : [1] C. Chevalley, Theory of Lie groups I, Princeton Univ. Press, 1946.
[2] H. Grauert, On Levi's problem and the imbedding of real analytic manifolds, Ann. of Math., 68 (1958), 460-472.
[3] V. W. Guillemin and S. Sternberg, Remarks on a paper of Hermann, Trans. Amer. Math. Soc., 130 (1968), 110-116.
[4] W. C. Hsiang and W. Y. Hsiang, Differentiable actions of compact connected classical groups I, Amer. J. Math., 89 (1967), 705-786.
[5] A. Nakanishi and F. Uchida, Actions of symplectic groups on certain manifolds, Tôhoku Math. J., 36 (1984), 81-98.
[6] R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc., 22, 1957.
[7] F. Uchida, Real analytic SL(n, R) actions on spheres, Tohoku Math. J., 33 (1981), 145-175.
[8] F. Uchida, Real analytic SL(n, C) actions, Bull. Yamagata Univ. Nat. Sci., 10 (1980), 1-14.
[9] F. Uchida, Actions of special linear groups on a product manifold, Bull. Yamagata Univ. Nat. Sci., 10 (1982), 227-233.
[10] F. Uchida, On the non-existence of smooth actions of complex symplectic group on cohomology quaternion projective spaces, Hokkaido Math. J., 12 (1983), 226-236.
[11] T. Wada, Smooth Sp(n) actions on cohomology quaternion projective spaces, Tôhoku Math. J., 29 (1977), 375-384.
[12] H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., 36 (1934), 63-89.

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