  The SU(4)-instanton equations are natural BPS equations for instantons on
8-manifolds. We study these equations on nearly Kaehler and Calabi-Yau torsion
manifolds of the form M x G/H, with G/H a coset space and M a product of a
torus with Euclidean space. By imposing G-invariance the instanton equations
reduce to interesting equations on M; for example, equations used by Kapustin
and Witten in the geometric Langlands program arise in this way. We carry out
reductions in a number of examples, and where possible present simple
solutions.
