The group orthogonality theorem applies to a finite group 
of group order 
and pairwise inequivalent irreducible
representations 
on complex vector
spaces of dimensions 
. Choose realizations by unitary
matrices. Then
 |
where the sum is over all group elements 
, 
is the entry in row 
and column 
of the matrix 
, 
denotes complex conjugate,
and the 
symbols are Kronecker deltas. The proof is nontrivial
and may be found in Eyring et al. (1944).
