This is an announcement for the paper "On orthogonal matrices maximizing the 1-norm" by Teodor Banica, Benoit Collins, and Jean-Marc Schlenker. Abstract: 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. Archive classification: math.OA math.CO Remarks: 17 pages The source file(s), omx.tex: 34742 bytes, is(are) stored in gzipped form as 0901.2923.gz with size 11kb. The corresponding postcript file has gzipped size 98kb. Submitted from: banica@picard.ups-tlse.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.2923 or http://arXiv.org/abs/0901.2923 or by email in unzipped form by transmitting an empty message with subject line uget 0901.2923 or in gzipped form by using subject line get 0901.2923 to: math@arXiv.org.