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Carinena, Jose F.; Santander, Mariano

Representation groups for semiunitary projective representations of finite groups. (English) Zbl 0439.20006

J. Math. Phys. 20, 2168-2177 (1979).
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Cited in 5 Documents

MSC:

20C25 Projective representations and multipliers
20C35 Applications of group representations to physics and other areas of science
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)

Keywords:

semiunitary projective representations

Citations:

Zbl 0304.22010
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Full Text: DOI

References:

[1] M. Santander, ”Linealización de representaciones proyectivas semiunitarias de grupos,” Universidad de Valladolid, 1977.
[2] J. F. Cariñena and M. Santander, J. Math. Phys. 16, 1416 (1975).JMAPAQ0022-2488
[3] E. P. Wigner, Ann. Math. 40, 149 (1939); ANMAAH0003-486X
[4] also U. Ulhorn, Ark. Fysik 23, 307 (1962); AFYSA70365-2440
[5] V. Bargmann, J. Math. Phys. 5, 862 (1964).JMAPAQ0022-2488
[6] V. S. Varadarajan, Geometry of Quantum Theory (Van Nostrand, New York, 1968, 1970), Vols. I and II. · Zbl 0155.56802
[7] W. G. Harter, J. Math. Phys. 10, 739 (1969).JMAPAQ0022-2488
[8] I. M. Isaacs, Character Theory of Finite Groups (Academic, New York, 1976), pp. 176–7.
[9] For the more general case of Polish G and semiunitary representations, see, e.g., U. Cattaneo, Rep. Math. Phys. 9, 31 (1976) and references therein for the previous work; for finite G the results of this paper, of course, hold with some evident simplifications.RMHPBE0034-4877
[10] J. Schur, J. Reine Angew. Math. 127, 20 (1904); JRMAA80075-4102
[11] J. Schur, 132, 85 (1907); JRMAA80075-4102, J. Reine Angew. Math.
[12] J. Schur, 139, 155 (1911).JRMAA80075-4102, J. Reine Angew. Math.
[13] T. Janssen, J. Math. Phys. 13, 342 (1972).JMAPAQ0022-2488
[14] See, e.g., N. B. Backhouse, Physica 70, 505 (1970) and references therein; PHYSAG0031-8914
[15] also J. M. Levy-Leblond, ”Galilei Group and Galilean invariance,” in Group Theory and Its Applications, edited by E. Loebl (Academic, New York, 1971), Vol. II, and references therein.
[16] See, e.g., U. Cattaneo and A. Janner, J. Math. Phys. 15, 1155 (1974), and references therein. This paper deals with a more general case than finite groups.JMAPAQ0022-2488
[17] C. C. Moore, Trans. Am. Math. Soc. 113, 40, 64 (1964).TAMTAM0002-9947
[18] U. Cattaneo, J. Math. Phys. 19, 452 (1978).JMAPAQ0022-2488
[19] V. Bargmann, Ann. Math. 59, 1 (1954).ANMAAH0003-486X · Zbl 0055.10304 · doi:10.2307/1969831
[20] G. W. Mackey, Acta Math. 99, 265 (1968), Theorem 4.2.ACMAA80001-5962
[21] S. MacLane, Homology (Springer, Berlin, 1967).
[22] E. P. Wigner, Group Theory and Its Applications (Academic, New York, 1971), Sec. 26. Also L. Janssen and M. Boon, Theory of Finite Groups. Applications in Physics (North-Holland, Amsterdam, 1967);
[23] R. Shaw and J. Lever, Commun. Math. Phys. 38, 257 (1974).CMPHAY0010-3616
[24] J. O. Dimmock, J. Math. Phys. 4, 1307 (1963).JMAPAQ0022-2488
[25] U. Cattaneo, J. Math. Phys. 19, 767 (1978), Appendix B.JMAPAQ0022-2488
[26] J. Schur, J. Reine Angew. Math. 127, 20 (1904), Satz IV.JRMAA80075-4102
[27] See, e.g., Ref. 7, Lemma 3.
[28] L. Michel, ”Invariance in Q. M. and group extensions,” in Istanbul Lectures, 1962, edited by F. Gursey (Gordon & Breach, New York, 1964); · doi:10.1088/0305-4470/10/5/019
[29] C. J. Bradley and D. E. Wallis, Q. J. Math. (Oxford) 25, 85 (1974); · doi:10.1088/0305-4470/10/5/019
[30] P. Rudra, J. Math. Phys. 17, 509, 512 (1976); JMAPAQ0022-2488 · doi:10.1088/0305-4470/10/5/019
[31] P. M. Van den Broek, J. Phys. A. Math. Gen. 10, 649 (1977) and references therein. · doi:10.1088/0305-4470/10/5/019
[32] H. Bacry and J. M. Levy-Leblond, J. Math. Phys. 9, 1605 (1968).JMAPAQ0022-2488
[33] L. Michel, Ref. 21, p. 169.
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