On some double coset decompositions of complex semi-simple Lie groups
ジャーナル
フリー
1966 年 18 巻 1 号 p. 1-44
詳細
- Published: 1966 Received: 1965/03/06 Available on J-STAGE: 2006/09/26 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/09/26 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) A. Borel, Kählerien cosec spaces of semi-simple Lie groups, Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 1147-1151.
2) A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, I., Amer. J. Math., 80 (1958), 458-538.
3) R. Bott, Homogeneous vector bundles, Ann. Math., 66 (1957), 203-248.
4) F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France, 84 (1956), 97-205.
5) C. Chevalley, Sur certains groupes simples, Tohoku Math. J., 7 (1955), 14-66.
6) F. Gantmacher, Canonical representations of automorphisms of a complex semi-simple Lie group, Rec. Math. (Mat. Sb.), 5 (1939), 101-146.
7) F. Gantmacher, On the classifications of real simple Lie groups, Rec. Math. (Mat. Sb.), 5 (1939), 217-250.
8) F. Gantmacher, The theory of matrices I, II, Chelsea Publishing, New York, 1959.
9) Harish-Chandra, Representations of semi-simple Lie groups, IV, V, VI, Amer. J. Math. 77 (1955), 743-777, 78 (1956), 1-41, 564-628.
10) Harish-Chandra, Fourier transforms on a semi-simple Lie algebra I, II, Amer. J. Math., 79 (1957), 193-257, 653-686.
11) M. Gelfand and M. I. Graev, Unitary representations of real unimodular groups, Izv. Acad. Nauk SSSR. Ser. Mat., 17 (1953), 189-248, (Russian).
12) M. I. Graev, Unitary representations of real simple Lie groups, Trudy Moskov, Mat. Obšc., 7 (1958), 333-389, (Russian).
13) S. Helgason, Differential geometry and symmetric spaces, Academic Press, 1962.
14) N. Iwahori, Lie algebras and Chevalley groups, Lecture note given at University of Tokyo, 1964, mimeographed.
15) B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann, of Math., 74 (1961), 329-387.
16) H. Matsumoto, Quelques remarques sur les groupes algèbriques réels, Proc. Japan Acad., 40 (1964), 4-7.
17) S. Murakami, On the automorphisms of real semi-simple Lie algebras, J. Math. Soc. Japan, 4 (1952), 103-133; 5 (1953), 105-112.
18) W. Specht, Gruppentheorie, Springer, 1956.
19) M. Sugiura, Conjugate classes of Cartan subalgebras in real semi-simple Lie algebras, J. Math. Soc. Japan, 11 (1959), 375-434.
20) T. Hirai, On infinitesimal operators of irreducible representations of the Lorentz group of n-th order, Proc. Japrn Acad., 38 (1962), 83-87.
Right : [1] A. Borel, Kählerien cosec spaces of semi-simple Lie groups, Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 1147-1151.
[2] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, I., Amer. J. Math., 80 (1958), 458-538.
[3] R. Bott, Homogeneous vector bundles, Ann. Math., 66 (1957), 203-248.
[4] F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France, 84 (1956), 97-205.
[5] C. Chevalley, Sur certains groupes simples, Tôhoku Math. J., 7 (1955), 14-66.
[6] F. Gantmacher, Canonical representations of automorphisms of a complex semi-simple Lie group, Rec. Math. (Mat. Sb.), 5 (1939), 101-146.
[7] F. Gantmacher, On the classifications of real simple Lie groups, Rec. Math. (Mat. Sb.), 5 (1939), 217-250.
[8] F. Gantmacher, The theory of matrices I, II, Chelsea Publishing, New York, 1959.
[9] Harish-Chandra, Representations of semi-simple Lie groups, IV, V, VI, Amer. J. Math. 77 (1955), 743-777, 78 (1956), 1-41, 564-628.
[10] Harish-Chandra, Fourier transforms on a semi-simple Lie algebra I, II, Amer. J. Math., 79 (1957), 193-257, 653-686.
[11] M. Gelfand and M. I. Graev, Unitary representations of real unimodular groups, Izv. Acad. Nauk SSSR. Ser. Mat., 17 (1953), 189-248, (Russian).
[12] M. I. Graev, Unitary representations of real simple Lie groups, Trudy Moskov, Mat. Obšc., 7 (1958), 333-389, (Russian).
[13] S. Helgason, Differential geometry and symmetric spaces, Academic Press, 1962.
[14] N. Iwahori, Lie algebras and Chevalley groups, Lecture note given at University of Tokyo, 1964, mimeographed.
[15] B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann, of Math., 74 (1961), 329-387.
[16] H. Matsumoto, Quelques remarques sur les groupes algèbriques réels, Proc. Japan Acad., 40 (1964), 4-7.
[17] S. Murakami, On the automorphisms of real semi-simple Lie algebras, J. Math. Soc. Japan, 4 (1952), 103-133; 5 (1953), 105-112.
[18] W. Specht, Gruppentheorie, Springer, 1956.
[19] M. Sugiura, Conjugate classes of Cartan subalgebras in real semi-simple Lie algebras, J. Math. Soc. Japan, 11 (1959), 375-434.
[20] T. Hirai, On infinitesimal operators of irreducible representations of the Lorentz group of n-th order, Proc. Japrn Acad., 38 (1962), 83-87.
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