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arXiv · 2008.02525

Automorphic vector bundles on the stack of $G$-zips

Naoki Imai·Jean-Stefan Koskivirta
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Abstract

For a connected reductive group $G$ over a finite field, we study automorphic vector bundles on the stack of $G$-zips. In particular, we give a formula in the general case for the space of global sections of an automorphic vector bundle in terms of the Brylinski--Kostant filtration. Moreover, we give an equivalence of categories between the category of automorphic vector bundles on the stack of $G$-zips and a category of admissible modules with actions of a zero-dimensional algebraic subgroup a Levi subgroup and monodromy operators.

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BibTeXRIS

Naoki Imai, Jean-Stefan Koskivirta. 2020-08-06. Automorphic vector bundles on the stack of $G$-zips. https://doi.org/10.1017/fms.2021.32

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