Discrete Unitary Invariance
  We show that certain determinantal functions of multiple matrices, when summed over the symmetries of the cube, decompose into functions of the original matrices. These are shown to be true in complete generality; that is, no properties of the underlying vector space will be used apart from normal ring properties, and therefore hold in any commutative ring. All proofs are elementary --- in fact, the majority are simply derivations. 
Adam W. Marcus
math.CO