Indices of Coincidence Isometries of the Hyper Cubic Lattice $Z^n$

Abstract

The problem of computing the index of a coincidence isometry of the hyper cubic lattice ${\mathbb{Z}}^n$ is considered. The normal form of a rational orthogonal matrix is analyzed in detail, and explicit formulas for the index of certain coincidence isometries of ${\mathbb{Z}}^n$ are obtained. These formulas generalize the known results for $n\le 4$.

AMS-Latex, preprint 10 pages