Complex generalised weighing matrices in centraliser algebras of monomial representations

Ronan Egan, Padraig Ó Catháin, Andrea Švob

An $n\times n$ matrix $W$ with exactly $w$ non-zero entries taken from the set of $k^{\mathrm{th}}$ complex roots of unity in each row and column satisfying $W{W}^{\ast }=w{I}_n$ is a com…