A computational study of certain Weyl modules for type G2 in characteristic 2

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-09-03 DOI:10.1016/j.jalgebra.2025.08.022

Stephen Doty

引用次数: 0

Abstract

Using the WeylModules GAP Package, we compute structural information about certain Weyl modules for type

G_{2}

in characteristic 2. This gives counterexamples to two conjectures stated by S. Donkin in 1990. It also illustrates capabilities of the package, which can in principle be applied to Weyl modules for any simple, simply-connected algebraic group in any characteristic, subject of course to time and space limitations of computational resources.

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特征2中G2型某些Weyl模的计算研究

使用WeylModules GAP包，我们计算了特征2中类型G2的某些Weyl模块的结构信息。这为S. Donkin在1990年提出的两个猜想提供了反例。它还说明了包的功能，原则上可以应用于Weyl模块，用于任何简单的、具有任何特征的单连通代数群，当然要受计算资源的时间和空间限制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.