Generalized holonomy of M-theory vacua

The number of M-theory vacuum supersymmetries, 0⩽n⩽32, is given by the number of singlets appearing in the decomposition of the 32 of SL(32,R) under H⊂SL(32,R) where H is the holonomy group of the generalized connection which incorporates non-vanishing 4-form. Here we compute this generalized holonomy for the n=16 examples of the M2-brane, M5-brane, M-wave, M-monopole, for a variety of their n=8 intersections and also for the n>16 pp-waves.