[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. |