Tables for
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 1.2, p. 57


T. Janssena*

aInstitute for Theoretical Physics, University of Nijmegen, 6524 ED Nijmegen, The Netherlands
Correspondence e-mail:

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Irreducible representations for cyclic groups [C_{n}]

[\omega =\exp (2\pi i/n)], s.c.m = smallest common multiple.

Order1ns.c.m.(n, 2)s.c.m.(n, 3)[\ldots]n
[ \Gamma_{1}] 1 1 1 1 [\ldots] 1
[\Gamma_{2}] 1 [\omega] [\omega^{2}] [\omega^{3}] [\ldots] [\omega^{-1}]
[\vdots] 1 [\vdots] [\vdots] [\vdots] [\ddots] [\vdots]
[\Gamma_{n}] 1 [\omega^{-1}] [\omega^{-2}] [\omega^{-3}] [\ldots] [\omega]