Mod p decompositions of gauge groups

We give mod p decompositions of homotopy types of the gauge groups of principal bundles over spheres, which are compatible with mod p decompositions of Lie groups given by Mimura, Nishida and Toda. As an application, we also give some computations on the homotopy types of gauge groups. In particular, we show the p-local converse of the result of Sutherland on the classifications of the gauge groups of principal SU(n)-bundles.