Abstract
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.
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