Duals of crystallographic groups. Band and quasi-band representations (Q1803539)

The dual of a crystallographic group is the set of equivalence classes of its unitary irreducible representations. The one-dimensional crystallographic groups show the necessity of introducing band and quasi- band representations, the word band being reserved for induced representations. The dual of the group F222 [No. 22 in the International Tables for Crystallography (T. Hahn (ed.), Reidel, 1987] is explicitly constructed. The author also surveys the most important aspects of the representation theory. He intends to discuss the case of multiple branches band representations of the crystallographic groups which promises further difficulties.