Dual Cones and the Voronoi Algorithm

Abstract

Max Koecher's axiomatic treatment of self-dual cones is generalized to pairs of dual cones. This leads to a powerful algorithm, à la Voronoi, to calculate the normalizer $N_{\GL_n(\funnyZ )}(G)$ and to decide conjugacy in $\GL_n(\funnyZ )$ for finite unimodular groups $G\leq \GL_n(\funnyZ )$.