Existence of a non-inductive linear form on certain solvable Lie algebras

Takaaki NOMURA

doi:10.2969/jmsj/03940667

Takaaki NOMURA

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 4 Pages 667-675

DOI https://doi.org/10.2969/jmsj/03940667

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Published: 1987 Received: April 23, 1986 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) J. Boidol, *-regularity of exponential Lie groups, Invent. Math., 56 (1980), 231-238.
2) H. Fujiwara, Sur le dual d'un groupe de Lie résoluble exponentiel, J. Math. Soc. Japan, 36 (1984), 629-636.
3) F. W. Keene, Square integrable representations and a Plancherel theorem for parabolic subgroups, Trans. Amer. Math. Soc., 243 (1978), 61-73.
4) D. Poguntke, Nichtsymmetrische sechsdimensionale Liesche Gruppen, J. Reine Angew. Math., 306 (1979), 154-176.
5) D. Poguntke, Symmetry and nonsymmetry for a class of exponential Lie groups, J. Reine Angew. Math., 315 (1980), 127-138.
6) D. Poguntke, Algebraically irreducible representations of L¹-algebras of exponential Lie groups, Duke Math. J., 50 (1983), 1077-1106.
7) I. I. Pyatetskii-Shapiro, Automorphic functions and the geometry of classical domains, Gordon and Breach, New York, 1969.
8) H. Rossi, Lectures on representations of groups of holomorphic transformations of Siegel domains, Lecture Note, Brandeis Univ., 1972.
9) H. Rossi and M. Vergne, Representations of certain solvable Lie groups on Hilbert spaces of holomorphic functions and the application to the holomorphic discrete series of a semisimple Lie group, J. Functional Analysis, 13 (1973), 324-389.
10) P. Tauvel, Sur la bicontinuité de l'application de Dixmier pour les algèbres de Lie résolubles, Ann. Fac. Sci. Toulouse, 4 (1982), 291-308.
11) G. Warner, Harmonic analysis on semi-simple Lie groups, I, Springer, Berlin, 1972.

Right : [1] J. Boidol, *-regularity of exponential Lie groups, Invent. Math., 56 (1980), 231-238.
[2] H. Fujiwara, Sur le dual d'un groupe de Lie résoluble exponentiel, J. Math. Soc. Japan, 36 (1984), 629-636.
[3] F. W. Keene, Square integrable representations and a Plancherel theorem for parabolic subgroups, Trans. Amer. Math. Soc., 243 (1978), 61-73.
[4] D. Poguntke, Nichtsymmetrische sechsdimensionale Liesche Gruppen, J. Reine Angew. Math., 306 (1979), 154-176.
[5] D. Poguntke, Symmetry and nonsymmetry for a class of exponential Lie groups, J. Reine Angew. Math., 315 (1980), 127-138.
[6] D. Poguntke, Algebraically irreducible representations of L¹-algebras of exponential Lie groups, Duke Math. J., 50 (1983), 1077-1106.
[7] I. I. Pyatetskii-Shapiro, Automorphic functions and the geometry of classical domains, Gordon and Breach, New York, 1969.
[8] H. Rossi, Lectures on representations of groups of holomorphic transformations of Siegel domains, Lecture Note, Brandeis Univ., 1972.
[9] H. Rossi and M. Vergne, Representations of certain solvable Lie groups on Hilbert spaces of holomorphic functions and the application to the holomorphic discrete series of a semisimple Lie group, J. Functional Analysis, 13 (1973), 324-389.
[10] P. Tauvel, Sur la bicontinuité de l'application de Dixmier pour les algèbres de Lie résolubles, Ann. Fac. Sci. Toulouse, 4 (1982), 291-308.
[11] G. Warner, Harmonic analysis on semi-simple Lie groups, I, Springer, Berlin, 1972.

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