Homogeneous ACM bundles on isotropic Grassmannians

TL;DR

This paper classifies all homogeneous arithmetically Cohen-Macaulay bundles on isotropic Grassmannians of types B, C, and D, showing finiteness and providing explicit characterizations based on highest weights.

Contribution

It extends the classification of homogeneous ACM bundles to isotropic Grassmannians, using step matrices and combining previous results on usual Grassmannians.

Findings

Finitely many irreducible homogeneous ACM bundles exist on these Grassmannians.

All such bundles can be classified via highest weights and step matrices.

Special highest weight bundles have succinct characterizations.

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.