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

International Tables for Crystallography (2013). Vol. D, ch. 1.2, pp. 70-71

Section 1.2.8. Glossary

T. Janssena*

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

1.2.8. Glossary

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[{\rm T}_{i_1 \ldots i_n}] tensor of rank n
[O(n)] orthogonal group
[{\bb Z}] ring of integers
[{\bf e}_i] basis vectors
g metric tensor
K point group
R orthogonal transformation
[C_m] cyclic group of order m
[SO(n)] special orthogonal group
[{\bb Z}^+] positive integers
[D_n] dihedral group of order n
E unit transformation, matrix or element
I inversion
[D(K)] representation of K
[\Gamma (K)] matrix representation of K
[|K|] order of K
[\oplus] sum of spaces or operators
[\otimes] tensor product
[\in] element of
[{\bf a}_i] basis of space or lattice
[V^*] dual space
S basis transformation
[\chi] character
[\chi (R)] value of [\chi] at R
[C_i] conjugacy class
[\chi_{\alpha}] irreducible character
[m_{\alpha}] multiplicity
N order of K
[d_{\alpha}] dimension of irreducible representation [\alpha]
[n_i] order of class [C_i]
[c_{ijk}] class multiplication constants
T tetrahedral group
O octahedral group
I icosahedral group
[P(K)] projective representation
[W_i (A_1 ,\ldots ,A_p )] word in generators [A_j]
[K^{d}] double group
[E(n)] Euclidean group
[g=\{R|{\bf a}\}] element of [E(n)]
[T(n)] translation group in n dimensions
[\Lambda] lattice
[\Lambda^*] reciprocal lattice
[{\bf a}(R)] translation vector system
[{\bf k}] vector in dual space
[G_{{\bf k}}] group of [{\bf k}]
[K_{{\bf k}}] point group of [G_{\bf {k}}]
[\omega] factor system
Det(R) determinant of R
[\left.\left(\matrix{ \alpha & \beta \cr i & j }\right| \matrix {\gamma &\cr k&\ell }\right)\hfill] Clebsch–Gordan coefficients
[\theta] time-reversal operator

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