Automorphic vector bundles on the stack of G-zips

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 0-dimensional algebraic subgroup a Levi subgroup and monodromy operators.

Keywords

• 14G35
• 20G40