On realization of the discrete series for semisimple Lie groups

Ryoshi HOTTA

doi:10.2969/jmsj/02320384

Ryoshi HOTTA

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JOURNAL FREE ACCESS

1971 Volume 23 Issue 2 Pages 384-407

DOI https://doi.org/10.2969/jmsj/02320384

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Published: 1971 Received: September 14, 1970 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Etudes Sci. Publ, Math., 25 (1965), 313-362.
2) V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math., 48 (1947), 568-640.
3) Harish-Chandra, Representations of semisimple Lie groups IV, Amer. J. Math., 77 (1955), 743-777.
4) Harish-Chandra, Representations of semisimple Lie groups V, Amer. J. Math., 78 (1956), 1-41.
5) Harish-Chandra, Discrete series for semisimple Lie groups I, Acta Math., 113 (1965), 241-318.
6) Harish-Chandra, Discrete series for semisimple Lie groups II, Acta Math., 116 (1966), 1-111.
7) S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
8) R. Hotta, Elliptic complexes on certain homogeneous spaces, Osaka J. Math., 7 (1970), 117-160.
9) R. Hotta, A remark on the Laplace-Beltrami operators attached to hermitian symmetric pairs, Osaka J. Math., 8 (1971), 15-19.
10) R. Hotta, On realization of the discrete series for semisimple Lie groups, Proc. Japan Acad., 46 (1970), 993-996.
11) M. S. Narasimhan and K. Okamoto, An analogue of the Borel-Weil-Bott theorem for hermitian symmetric pairs of non-compact type, Ann. of Math., 91 (1970), 486-511.
12) K. Okamoto, On induced representations, Osaka J. Math., 4 (1967), 85-94.
13) K. Okamoto and H. Ozeki, On square-integrable ∂-cohomology spaces attached to Hermitian symmetric spaces, Osaka J. Math., 4 (1967), 95-110.
14) W. Schmid, Homogeneous complex manifolds and representations of semisimple Lie groups, Thesis, Proc. Nat. Acad. Sci. U.S.A., 59 (1968), 56-59.
15) W. Schmid, On a conjecture of Langlands, Ann. of Math., 93 (1971), 1-42.
16) R. Takahashi, Sur les représentations unitaires des groupes de Lorentz généralisés,Bull. Soc. Math. France, 91 (1963), 289-433.

Right : [1] A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Etudes Sci. Publ, Math., 25 (1965), 313-362.
[2] V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math., 48 (1947), 568-640.
[3] Harish-Chandra, Representations of semisimple Lie groups IV, Amer. J. Math., 77 (1955), 743-777.
[4] Harish-Chandra, Representations of semisimple Lie groups V, Amer. J. Math., 78 (1956), 1-41.
[5] Harish-Chandra, Discrete series for semisimple Lie groups I, Acta Math., 113 (1965), 241-318.
[6] Harish-Chandra, Discrete series for semisimple Lie groups II, Acta Math., 116 (1966), 1-111.
[7] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
[8] R. Hotta, Elliptic complexes on certain homogeneous spaces, Osaka J. Math., 7 (1970), 117-160.
[9] R. Hotta, A remark on the Laplace-Beltrami operators attached to hermitian symmetric pairs, Osaka J. Math., 8 (1971), 15-19.
[10] R. Hotta, On realization of the discrete series for semisimple Lie groups, Proc. Japan Acad., 46 (1970), 993-996.
[11] M. S. Narasimhan and K. Okamoto, An analogue of the Borel-Weil-Bott theorem for hermitian symmetric pairs of non-compact type, Ann. of Math., 91 (1970), 486-511.
[12] K. Okamoto, On induced representations, Osaka J. Math., 4 (1967), 85-94.
[13] K. Okamoto and H. Ozeki, On square-integrable ∂-cohomology spaces attached to Hermitian symmetric spaces, Osaka J. Math., 4 (1967), 95-110.
[14] W. Schmid, Homogeneous complex manifolds and representations of semisimple Lie groups, Thesis, Proc. Nat. Acad. Sci. U. S. A., 59 (1968), 56-59.
[15] W. Schmid, On a conjecture of Langlands, Ann. of Math., 93 (1971), 1-42.
[16] R. Takahashi, Sur les représentations unitaires des groupes de Lorentz généralisés,Bull. Soc. Math. France, 91 (1963), 289-433.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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