2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61081In this note we prove that the moduli space of rank $2n$ symplectic instanton bundles on ${\PP^{2n+1}}$, defined from the well known monad condition, is affine. This result was not known even in the case $n=1$, where the real instanton bundles correspond to self dual Yang Mills $Sp(1)$-connections over the 4-dimensional sphere. The result is proved as a consequence of the existence of an invariant of the multidimensional matrices representing the instanton bundles.9 pages, Latex 2eAlgebraic Geometry14D21, 14J60, 15A72text