International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 1.5, pp. 162-188   | 1 | 2 |
https://doi.org/10.1107/97809553602060000553

Chapter 1.5. Crystallographic viewpoints in the classification of space-group representations

M. I. Aroyoa* and H. Wondratschekb

a Faculty of Physics, University of Sofia, bulv. J. Boucher 5, 1164 Sofia, Bulgaria , and bInstitut für Kristallographie, Universität, D-76128 Karlsruhe, Germany
Correspondence e-mail:  aroyo@phys.uni-sofia.bg

References

First citation Altmann, S. L. (1977). Induced representations in crystals and molecules. London: Academic Press.Google Scholar
First citation Bouckaert, L. P., Smoluchowski, R. & Wigner, E. P. (1936). Theory of Brillouin zones and symmetry properties of wave functions in crystals. Phys. Rev. 50, 58–67.Google Scholar
First citation Boyle, L. L. (1986). The classification of space group representations. In Proceedings of the 14th international colloquium on group-theoretical methods in physics, pp. 405–408. Singapore: World Scientific.Google Scholar
First citation Boyle, L. L. & Kennedy, J. M. (1988). Raumgruppen Charakterentafeln. Z. Kristallogr. 182, 39–42.Google Scholar
First citation Bradley, C. J. & Cracknell, A. P. (1972). The mathematical theory of symmetry in solids: representation theory for point groups and space groups. Oxford: Clarendon Press.Google Scholar
First citation Cracknell, A. P., Davies, B. L., Miller, S. C. & Love, W. F. (1979). Kronecker product tables, Vol. 1, General introduction and tables of irreducible representations of space groups. New York: IFI/Plenum.Google Scholar
First citation Davies, B. L. & Cracknell, A. P. (1976). Some comments on and addenda to the tables of irreducible representations of the classical space groups published by S. C. Miller and W. F. Love. Acta Cryst. A32, 901–903.Google Scholar
First citation Davies, B. L. & Dirl, R. (1987). Various classification schemes for irreducible space group representations. In Proceedings of the 15th international colloquium on group-theoretical methods in physics, edited by R. Gilmore, pp. 728–733. Singapore: World Scientific.Google Scholar
First citation Delaunay, B. (1933). Neue Darstellung der geometrischen Kristallographie. Z. Kristallogr. 84, 109–149; 85, 332. (In German.)Google Scholar
First citation International Tables for Crystallography (2005). Vol. A. Space-group symmetry, edited by Th. Hahn, 5th ed. Heidelberg: Springer.Google Scholar
First citation Jan, J.-P. (1972). Space groups for Fermi surfaces. Can. J. Phys. 50, 925–927.Google Scholar
First citation Jansen, L. & Boon, M. (1967). Theory of finite groups. Applications in physics: symmetry groups of quantum mechanical systems. Amsterdam: North-Holland.Google Scholar
First citation Janssen, T. (2003). International tables for crystallography, Vol. D, Physical properties of crystals, edited by A. Authier, ch. 1.2, Representations of crystallographic groups. Dordrecht: Kluwer Academic Publishers.Google Scholar
First citation Kovalev, O. V. (1986). Irreducible and induced representations and co-representations of Fedorov groups. Moscow: Nauka. (In Russian.)Google Scholar
First citation Lomont, J. S. (1959). Applications of finite groups. New York: Academic Press.Google Scholar
First citation Miller, S. C. & Love, W. F. (1967). Tables of irreducible representations of space groups and co-representations of magnetic space groups. Boulder: Pruett Press.Google Scholar
First citation Raghavacharyulu, I. V. V. (1961). Representations of space groups. Can. J. Phys. 39, 830–840.Google Scholar
First citation Rosen, J. (1981). Resource letter SP-2: Symmetry and group theory in physics. Am. J. Phys. 49, 304–319.Google Scholar
First citation Slater, L. S. (1962). Quantum theory of molecules and solids, Vol. 2. Amsterdam: McGraw-Hill.Google Scholar
First citation Stokes, H. T. & Hatch, D. M. (1988). Isotropy subgroups of the 230 crystallographic space groups. Singapore: World Scientific.Google Scholar
First citation Stokes, H. T., Hatch, D. M. & Nelson, H. M. (1993). Landau, Lifshitz, and weak Lifshitz conditions in the Landau theory of phase transitions in solids. Phys. Rev. B, 47, 9080–9083.Google Scholar
First citation Wintgen, G. (1941). Zur Darstellungstheorie der Raumgruppen. Math. Ann. 118, 195–215. (In German.)Google Scholar
First citation Zak, J., Casher, A., Glück, M. & Gur, Y. (1969). The irreducible representations of space groups. New York: Benjamin.Google Scholar