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

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. D. ch. 2.1, p. 289

Table 2.1.3.6 

G. Eckolda*

a Institut für Physikalische Chemie, Universität Göttingen, Tammannstrasse 6, D-37077 Göttingen, Germany
Correspondence e-mail: geckold@gwdg.de

Table 2.1.3.6 | top | pdf |
Irreducible representations of the space group [P6 _3] for [{\bf q}={\bf c}^*/2] (the A point)

[P6_3] E [D_{60}^z ] [D_{120}^z ] [D_{180}^z ] [D_{240}^z] [D_{300}^z ]
[\tau ^{(1)}({{\bf c}^*/2}) ] 1 i 1 [i] 1 i
[\tau ^{(2)}({{\bf c}^*/2}) ] 1 [i\exp({i\pi /3}) = \exp({- i\pi /6}) ] [\exp({i2\pi /3}) ] [-i ] [\exp({i4\pi /3}) = \exp({- i2\pi /3}) ] [i\exp({-i\pi /3}) = \exp({ i\pi /6}) ]
[\tau ^{(3)}({{\bf c}^*/2}) ] 1 [i\exp({i2\pi /3})=\exp(i\pi/6) ] [\exp({i4\pi /3})=\exp(-i2\pi/3) ] [i] [\exp({i2\pi /3}) ] [i\exp({-i2\pi /3})=\exp(-i\pi/6) ]
[\tau ^{(4)}({{\bf c}^*/2}) ] 1 [-i ] 1 [-i ] 1 [-i ]
[\tau ^{(5)}({{\bf c}^*/2}) ] 1 [i\exp({-i2\pi /3})=\exp(-i\pi/6) ] [\exp({i2\pi /3}) ] [i] [\exp({i4\pi /3})=\exp(-i2\pi/3) ] [i\exp({i2\pi /3}) = \exp({i\pi /6}) ]
[\tau ^{(6)}({{\bf c}^*/2}) ] 1 [i\exp(-i\pi/3)=\exp({i\pi /6}) ] [\exp({i4\pi /3})=\exp(-i2\pi/3) ] [-i ] [\exp({i2\pi /3}) ] [i\exp({i\pi /3})=\exp(-i\pi/6) ]