On conjugacy of diagonalizable integral matrices
Number Theory
2019-10-15 v1 Combinatorics
Abstract
It is shown that under some additional assumption two diagonalizable integral matrices X and Y with only rational eigenvalues are conjugate in GL(n,Z) if and only if they are conjugate over all localizations. This is used to prove that for a prime p == 3 (mod 4) the adjacency matrices of the Paley graph and the Peisert graph on p^2 vertices are conjugate in GL(p^2,Z), answering a question by Peter Sin.
Keywords
Cite
@article{arxiv.1910.05974,
title = {On conjugacy of diagonalizable integral matrices},
author = {Gabriele Nebe},
journal= {arXiv preprint arXiv:1910.05974},
year = {2019}
}