BIORTHOGONAL SETS FOR ENERGY-BANDS IN SOLIDS

A biorthogonal set is constructed for a basis of a band representation. A simple fact is used that any band representation can be induced from a one-dimensional representation of a point group (the latter is not necessarily an isotropy group of a Wyckoff position). It is shown that the biorthogonal set has the same symmetry structure as the original basis of the band representation. Symmetry relations are established for the matrix connecting the biorthogonal set with the functions of the original basis.