We define automorphic vector bundles on the stack of $G$-zips introduced by Moonen-Pink-Wedhorn-Ziegler and study their global sections. In particular, we give a combinatorial condition on the weight for the existence of nonzero mod $p$ automorphic forms on Shimura varieties of Hodge-type. We attach to the highest weight of the representation $V(\lambda)$ a mod $p$ automorphic form and we give a modular interpretation of this form in some cases.查看全文