A remark of decompositions of the regular representations of semi-direct product groups

Satoshi KAWAKAMI

doi:10.2969/jmsj/03610121

Satoshi KAWAKAMI

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JOURNAL FREE ACCESS

1984 Volume 36 Issue 1 Pages 121-130

DOI https://doi.org/10.2969/jmsj/03610121

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Published: 1984 Received: January 26, 1983 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: SUBTITLE Details: Wrong : Dedicated to Professor Hisaaki Yoshizawa on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Dixmier, Les C^*-algèbres et leur représentations, Gauthier-Villars, Paris, 1968.
2) E. G. Effros, Transformation groups and C^*-algebras, Ann. of Math., 81(1965), 38-55.
3) S. Funakosi, On representations of non-type I groups, Tohoku Math. J., 31(1979), 139-150.
4) S. Funakosi, Different irreducible decompositions of unitary representations of locally compact non-type I groups, Math. Seminar Notes, Kobe Univ., 9(1981), 253-258.
5) J. Glimm, Locally compact transformation groups, Trans. AMS, 101(1961), 124-138.
6) S. Kawakami, Irreducible representations of non-regular semi-direct product groups, Math. Japon., 26(1981), 667-693.
7) S. Kawakami, On decompositions of some factor representations, Math. Japon., 27 (1982), 521-534.
8) S. Kawakami, Representations of the discrete Heisenberg group, Math. Japon., 27 (1982), 551-564.
9) S. Kawakami, A remark of decompositions of the regular representations of free groups, Math. Japon., 28(1983), 337-340.
10) S. Kawakami and T. Kajiwara, Representations of certain non-type I C^*-crossed products, Math. Japon., 27 (1982), 675-699.
11) S. Kawakami and T. Kajiwara, Weak cohomology and the diverse possibility of decompositions of representations, Math. Japon., 28 (1983), 181-186.
12) A. A. Kirillov, Elements of the theory of representations, Moscow, 1972.
13) G. W. Mackey, On induced representations of groups, Amer. J. Math., 73 (1951), 576-592.
14) G. W. Mackey, Induced representations of locally compact groups I, Ann. of Math., 55 (1952), 101-139.
15) G. W. Mackey, Induced representations and normal subgroups, Proc. Intern. Symp. on Linear Spaces, Jerusalem, 1960, 319-326.
16) G. W. Mackey, Borel structures in groups and their duals, Trans. AMS, 83 (1957), 134-165.
17) F. I. Mautner, Unitary representations of locally compact groups I, Ann. of Math., 51(1950), 1-25.
18) T. Pytlik, Radial functions on free groups and a decomposition of the regular representation into irreducible components, J. Reine Angew. Math., 326(1981), 124-135.
19) M. Saito, Représentation unitaires monomiales d'un groupe discret, en particulier du groupe modulaire, J. Math. Soc. Japan, 26 (1974), 464-482.
20) H. Yoshizawa, Some remarks on unitary representations of the free group, Osaka Math. J., 3(1951), 55-63.

Right : [1] J. Dixmier, Les C-algèbres et leur représentations, Gauthier-Villars, Paris, 1968.
[2] E. G. Effros, Transformation groups and C-algebras, Ann. of Math., 81 (1965), 38-55.
[3] S. Funakosi, On representations of non-type I groups, Tôhoku Math. J., 31 (1979), 139-150.
[4] S. Funakosi, Different irreducible decompositions of unitary representations of locally compact non-type I groups, Math. Seminar Notes, Kobe Univ., 9 (1981), 253-258.
[5] J. Glimm, Locally compact transformation groups, Trans. AMS, 101 (1961), 124-138.
[6] S. Kawakami, Irreducible representations of non-regular semi-direct product groups, Math. Japon., 26 (1981), 667-693.
[7] S. Kawakami, On decompositions of some factor representations, Math. Japon., 27 (1982), 521-534.
[8] S. Kawakami, Representations of the discrete Heisenberg group, Math. Japon., 27 (1982), 551-564.
[9] S. Kawakami, A remark of decompositions of the regular representations of free groups, Math. Japon., 28 (1983), 337-340.
[10] S. Kawakami and T. Kajiwara, Representations of certain non-type I C-crossed products, Math. Japon., 27 (1982), 675-699.
[11] S. Kawakami and T. Kajiwara, Weak cohomology and the diverse possibility of decompositions of representations, Math. Japon., 28 (1983), 181-186.
[12] A. A. Kirillov, Elements of the theory of representations, Moscow, 1972.
[13] G. W. Mackey, On induced representations of groups, Amer. J. Math., 73 (1951), 576-592.
[14] G. W. Mackey, Induced representations of locally compact groups I, Ann. of Math., 55 (1952), 101-139.
[15] G. W. Mackey, Induced representations and normal subgroups, Proc. Intern. Symp. on Linear Spaces, Jerusalem, 1960, 319-326.
[16] G. W. Mackey, Borel structures in groups and their duals, Trans. AMS, 83 (1957), 134-165.
[17] F. I. Mautner, Unitary representations of locally compact groups I, Ann. of Math., 51 (1950), 1-25.
[18] T. Pytlik, Radial functions on free groups and a decomposition of the regular representation into irreducible components, J. Reine Angew. Math., 326 (1981), 124-135.
[19] M. Saito, Représentation unitaires monomiales d'un groupe discret, en particulier du groupe modulaire, J. Math. Soc. Japan, 26 (1974), 464-482.
[20] H. Yoshizawa, Some remarks on unitary representations of the free group, Osaka Math. J., 3 (1951), 55-63.

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