Homogeneous ACM bundles on isotropic Grassmannians

Abstract

Abstract In this paper, we characterize homogeneous arithmetically Cohen–Macaulay (ACM) bundles over isotropic Grassmannians of types 𝐵, 𝐶 and 𝐷 in terms 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 Miró-Roig. Moreover, if the irreducible initialized homogeneous ACM bundles correspond to some special highest weights, then they can be characterized by succinct forms.