Equivariant vector bundles on Drinfeld's halfspace over a finite field

2021/12/01 by Sascha Orlik, Orlik, Sascha
Mathematics · #14L30 #17B10 #20C33 #20G40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2112.00687

openalex publication_date 2021/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X ⊂ ℙ_k^d be Drinfeld's halfspace over a finite field k and let E be a homogeneous vector bundle on ℙ_k^d. The paper deals with two different descriptions of the space of global sections H⁰(X,E) as GL_d+1(k)-representation. This is an infinite dimensional modular representation. Here we follow the ideas of \citeO2,OS treating the p-adic case. As a replacement for the universal enveloping algebra we consider both the crystalline universal enveloping algebra and the ring of differential operators on the flag variety with respect to E.

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