Irreducible Representations of Translation Group Brillouin Zone

2 Irreducible Representations of Translation Group. Brillouin Zone 

There are A = A1A2A3 sets of integers pi,P2,Ps (p = 0,1. A — 1) that are used to label N different irreps of the translation group T  

Introducing the primitive translation vectors 81,82,83 of the reciprocal lattice 

The A irreps of T ) are now labeled by the A allowed fc vectors.The point symmetry of reciprocal lattice coincides with that of the direct one. However, the type of reciprocal lattice may differ from that of the direct lattice. 

A pair of vectors fc and k = k + 8m is said to be equivalent since the irrep of T i described by fc can be equally well described by fc. Therefore, the label fc is 

---