  For $U\in O(N)$ we have $||U||_1\leq N\sqrt{N}$, with equality if and only if
$U=H/\sqrt{N}$, with $H$ Hadamard matrix. Motivated by this remark, we discuss
in this paper the algebraic and analytic aspects of the computation of the
maximum of the 1-norm on O(N). The main problem is to compute the $k$-th moment
of the 1-norm, with $k\to\infty$, and we present a number of general comments
in this direction.
