2014 Les produits directs Dkp x Dmq de représentations irréductibles du groupe double O4h de Cu2O sont réduits. Les vecteurs k, m prennent les valeurs correspondant aux quatre points de plus haute symétrie de la zone de Brillouin. Dkp et Dmq sont des représentations toutes deux soit simples soit doubles. Les carrés symétrisés des représentations Dkp sont également réduits. Abstract.-The direct products Dkp Dmq of irreducible représentations of the double space group O4h of Cu2O are reduced. The wave vectors k, m run over the four highest symmetry points of the Brillouin zone. Dkp and Dmq are taken to be both the single or both the double-valued representations. The symmetrized squares of the représentations Dkp are reduced too.
A detailed example of the method of finding representations of a space group with the help of the ab.stract definition of the group is given. A list of all the irreducible representations of the double space groups D;h -Dif; is presented.Mit Hilfe der abstrakten Definition der Gruppe wird ein Beispiel zur Best,immung der Darstellungen einer Raumgruppe behandelt: Es wird eine Tabelle aller irreduziblen Darstellungen der Doppelgruppen D&, -D:: angegeben.
The paper presents selection rules for the double space group O4 h of cuprite, i.e. decompositions of direct products of the irreducible representations in which one factor refers to a high symmetry point and the other to a symmetry line of the Brillouin zone
A method of finding the irreducible representations of the single and double space groups is described based directly on the abstract definition of the group.
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