2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229889By using properties of the Young orthogonal representation, this paper derives a simple form for the Fourier transform of permutations acting on the homogeneous space of $n$-dimensional vectors, and shows that the transform requires $2n-2$ multiplications and the same number of additions.Fixed title, found some errors in the math of the previous version (not serious)Representation TheoryGroup Theory43A32,43A65text