2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186547We formulate a theory for N=4 supersymmetric Yang-Mills multiplet in a non-adjoint representation R of SO(N) as an important application of our recently-proposed model for N=1 supersymmetry. This system is obtained by dimensional reduction from an N=1 supersymmetric Yang-Mills multiplet in non-adjoint representation in ten dimensions. The consistency with supersymmetry requires that the non-adjoint representation R with the indices i, j, ... satisfy the three conditions η^{i j} = δ^{i j}, (T^I)^{i j} = - (T^I)^{j i} and (T^I)^{[ i j |} (T^I)^{| k ] l} = 0 for the metric η^{i j} and the generators T^I, which are the same as the N=1 case.6 pages, no figures, accepted for publication in Phys. Rev. DHigh Energy Physics - Theorytext