Homogeneous ACM bundles on isotropic Grassmannians

Abstract

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles over isotropic Grassmannians of types $B$, $C$ and $D$ in term of step matrices. We show that there are only finitely many irreducible homogeneous ACM bundles by twisting line bundles over these isotropic Grassmannians. So we classify all homogeneous ACM bundles over isotropic Grassmannians combining the results on usual Grassmannians by Costa and Mir{\'o}-Roig. Moreover, if the irreducible initialized homogeneous ACM bundles correspond to some special highest weights, then they can be characterized by succinct forms.