All the irreducible band representations of a space group are shown to be induced from a set of inequivalent relevant symmetry centers in the Wigner-Seitz cell. A connection is established between representations and band representations of space groups by using the Born—von Kármán boundary conditions. Continuity chords are used for proving the equivalency theorem which enables one to distinguish between equivalent and inequivalent band representations. As examples we consider a one-dimensional crystal and the $D_{6h}^4$ space group for a hexagonal close-packed structure.

• Received 6 August 1981

DOI:https://doi.org/10.1103/PhysRevB.26.3010