$G$ -zips栈上的自守向量丛
Automorphic vector bundles on the stack of $G$-zips
摘要：
对于有限域上的连通约化群$G$，研究了$G$ -拉链堆叠上的自守向量丛.特别地，我们给出了一般情况下自同构向量丛的整体瓣空间的Brylinski-Kostant滤子公式.此外，我们给出了$G$ -zips栈上的自同构向量丛范畴与具有零维代数子群、Levi子群和monodromy算子作用的容许模范畴的范畴等价性.
英文摘要：
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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