On discrete subgroups of the Lorentz group

1. E. P. Wigner:Ann. of Math.,40, 149 (1939).

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2. I. M. Gelfand, R. A. Minlos andZ. Ya. Shapiro:Representations of the Rotation and Lorentz Groups and Their Applications (Oxford and New York, N. Y., 1963);M. A. Naimark:Linear Representations of the Lorentz Group (London, 1964). These are two standard references on this subject. It is not our intention to give a complete list of the relevant literature which would probably fill several dozens of pages.

3. R. Fricke andF. Klein:Vorlesungen über die Theorie der elliptischen Modulfunktionen, Vol.1 (Leipzig, 1890); Vol.2 (Leipzig, 1892).Vorlesungen über die Theorie der automorphen Funktionen, Vol.1 (Leipzig, 1897); Vol.2, part 1 (Leipzig, 1901); part 2 (Leipzig, 1912). These books have been reprinted by the Johnson Reprint Corporation (New York, N.Y., 1966).

4. L. R. Ford:Automorphic Functions (New York, N. Y., 1972).

5. J. Lehner:A Short Course in Automorphic Functions (New York, N. Y., 1966).

6. I. M. Gelfand, M. I. Graev andI. I. Pyatetskii-Shapiro:Representation Theory and Automorphic Functions (Philadelphia, Pa., 1966).

7. A four-vector has the components (x ₁, x₂, x₃, x₆). We use the metricx ²₁ +x ²₂ +x ²₃ −x ²₀ in agreement with the book byNAIMARK which is quoted under ref. (2).I. M. Gelfand, R. A. Minlos andZ. Ya. Shapiro:Representations of the Rotation and Lorentz Groups and Their Applications (Oxford and New York, N. Y., 1963);M. A. Naimark:Linear Representations of the Lorentz Group (London, 1964). These are two standard references on this subject. It is not our intention to give a complete list of the relevant literature which would probably fill several dozens of pages.

8. J. Neubüser, H. Wondratschek andR. Bülow:Acta Cryst., A27, 517, 520, 523 (1971).

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9. E. Ascher andA. Janner:Helv. Phys. Acta,38, 551 (1965);Comm. Math. Phys.,11, 138 (1968).

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