Homogeneous ACM bundles on a Grassmannian

In this paper, we characterize homogeneous arithmetically Cohen–Macaulay (ACM, for short) bundles on Grassmannians Gr(k,n)Gr(k,n) and we construct irreducible families of indecomposable ACM bundles on a Grassmannian Gr(k,n)Gr(k,n) of arbitrary high rank and dimension.As a consequence we prove that all Grassmann varieties Gr(k,n)Gr(k,n) are of wild representation type unless the projective spaces Gr(0,n)Gr(0,n) and Gr(n−1,n)Gr(n−1,n) and the hyperquadric Gr(1,3)Gr(1,3) in P5P5 which are of finite representation type.