Table 2.1.3.5

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

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

G. Eckold^a ^*

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

Table 2.1.3.5 | top | pdf |
Irreducible representations of the space group [P6_3] for $[{\bf q}={\bf 0}]$ (the $[\Gamma]$ point)

	E	$[D_{60}^z ]$	$[D_{120}^z ]$	$[D_{180}^z ]$	$[D_{240}^z ]$	$[D_{300}^z ]$
$[\tau^{(1)}({\bf 0}) ]$	1	1	1	1	1	1
$[\tau^{(2)}({\bf 0}) ]$	1	$[\exp({i\pi /3}) ]$	$[\exp({i2\pi /3}) ]$		$[\exp({i4\pi /3}) = \exp({- i2\pi /3}) ]$	$[\exp({i5\pi /3}) = \exp({- i\pi /3}) ]$
$[\tau^{(3)}({\bf 0}) ]$	1	$[\exp({i2\pi /3}) ]$	$[\exp({i4\pi /3}) =\exp(-i2\pi/3)]$	1	$[\exp({i2\pi /3}) ]$	$[\exp({i4\pi /3}) =\exp(-i2\pi/3)]$
$[\tau^{(4)}({\bf 0}) ]$	1		1		1
$[\tau^{(5)}({\bf 0}) ]$	1	$[\exp({i4\pi /3}) =\exp(-i2\pi/3)]$	$[\exp({i2\pi /3}) ]$	1	$[\exp({i4\pi /3}) =\exp(-i2\pi/3)]$	$[\exp({i2\pi /3}) ]$
$[\tau^{(6)}({\bf 0}) ]$	1	$[\exp({i5\pi /3}) =\exp(-i\pi/3)]$	$[\exp({i4\pi /3}) =\exp(-i2\pi/3)]$		$[\exp({i2\pi /3}) ]$	$[\exp({i\pi /3}) ]$