Generalized μ-ordinary Hasse invariants

We give a short proof for the existence of μ-ordinary Hasse invariants for the good reduction special fiber of Shimura varieties of Hodge-type using the stack of G-zips introduced by Moonen-Wedhorn and Pink-Wedhorn-Ziegler. We give an explicit formula for the power of the Hodge bundle that admits a Hasse invariant. When G is a Weil restriction of G1, we relate the Ekedahl-Oort strata of G and those of G1.