Homogeneous ACM bundles on Grassmannians of exceptional types

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles over homogeneous varieties of Picard rank one in terms of their associated data. This is a generalization of the result on homogeneous varieties of Picard rank one of classical types presented by Costa and Miró-Roig for type A, and Du, Fang, and Ren for types B,C and D. We show that there are only finitely many irreducible homogeneous ACM bundles by twisting line bundles over Grassmannians of exceptional types. As a consequence, we prove that some Grassmannians of exceptional types are of wild representation type.