Indices of coincidence isometries of the hypercubic lattice {\bb Z}^{n}

Abstract

The problem of computing the index of a coincidence isometry of the hypercubic lattice Z{n} is considered. The normal form of a rational orthogonal matrix is analyzed in detail and explicit formulas for the indices of certain coincidence isometries of Z{n} are obtained. These formulas generalize the known results for n < or = 4.