On the characters and equivalence of continuous series representations

Ronald L. LIPSMAN

doi:10.2969/jmsj/02330452

Ronald L. LIPSMAN

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1971 年 23 巻 3 号 p. 452-480

DOI https://doi.org/10.2969/jmsj/02330452

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Published: 1971 Received: 1970/08/11 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) Harish-Chandra, (a) The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc., 76 (1954), 485-528.
(b) The characters of semisimple Lie groups, Trans. Amer. Math. Soc., 78 (1956), 564-628.
(c) Fourier transforms on a semisimple Lie algebra I, Amer. J. Math., 79 (1957), 193-257.
(d) Some results on an invariant integral on a semisimple Lie algebra, Ann. of Math., 80 (1964), 551-593.
(e) Invariant eigendistributions on a semisimple Lie group, Trans. Amer. Math. Soc., 119 (1965), 457-508.
(f) Discrete series for semisimple Lie groups I, Acta Math., 113 (1965), 241-318.
(g) Two theorems on semisimple Lie groups, Ann. of Math., 83 (1966), 74-128.
(h) Discrete series for semisimple Lie groups II, Acta Math., 116 (1966), 1-111.
(i) Harmonic analysis on semisimple Lie groups, Amer. Math. Soc. Colloq. Lectures, 1969.
2) S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
3) T. Hirai, The characters of some induced representations of semisimple Lie groups, J. Math. Kyoto Univ., 8 (1968), 313-363.
4) R. Lipsman, The dual topology for the principal and discrete series on semi simple groups, Trans. Amer. Math. Soc., 152 (1970), 399-417.
5) G. Mackey, Unitary representations of group extensions I, Acta Math., 99 (1958), 265-311.
6) I. Satake, On representations and compactifications of symmetric Riemannian spaces, Ann. of Math., 71 (1960), 77-110.

Right : 1) This restriction has been removed. See footnote 4).
2) This is a consequence of the fact that for finite (indeed compact) extensions, the normal subgroup is always “regularly embedded”.
3) N. Bourbaki, Livre VI, Intégration, Ch. 7, p. 66.
[1] Harish-Chandra, (a) The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc., 76 (1954), 485-528.
[1] Harish-Chandra, (b) The characters of semisimple Lie groups, Trans. Amer. Math. Soc., 78 (1956), 564-628.
[1] Harish-Chandra, (c) Fourier transforms on a semisimple Lie algebra I, Amer. J. Math., 79 (1957), 193-257.
[1] Harish-Chandra, (d) Some results on an invariant integral on a semisimple Lie algebra, Ann. of Math., 80 (1964), 551-593.
[1] Harish-Chandra, (e) Invariant eigendistributions on a semisimple Lie group, Trans. Amer. Math. Soc., 119 (1965), 457-508.
[1] Harish-Chandra, (f) Discrete series for semisimple Lie groups I, Acta Math., 113 (1965), 241-318.
[1] Harish-Chandra, (g) Two theorems on semisimple Lie groups, Ann. of Math., 83 (1966), 74-128.
[1] Harish-Chandra, (h) Discrete series for semisimple Lie groups II, Acta Math., 116 (1966), 1-111.
[1] Harish-Chandra, (i) Harmonic analysis on semisimple Lie groups, Amer. Math. Soc. Colloq. Lectures, 1969.
[2] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
[3] T. Hirai, The characters of some induced representations of semisimple Lie groups, J. Math. Kyoto Univ., 8 (1968), 313-363.
[4] R. Lipsman, The dual topology for the principal and discrete series on semi simple groups, Trans. Amer. Math. Soc., 152 (1970), 399-417.
[5] G. Mackey, Unitary representations of group extensions I, Acta Math., 99 (1958), 265-311.
[6] I. Satake, On representations and compactifications of symmetric Riemannian spaces, Ann. of Math., 71 (1960), 77-110.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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