Locally quadratic modules and minuscule representations

TL;DR

This paper provides a new proof of a theorem demonstrating that for simple algebraic groups, modules with quadratic root actions decompose into sums of minuscule representations, clarifying their structure.

Contribution

The paper introduces a novel proof technique for Timmesfeld's theorem, enhancing understanding of modules with quadratic root actions in simple algebraic groups.

Findings

Modules with quadratic root actions are direct sums of minuscule representations

New proof simplifies understanding of the structure of such modules

Clarifies the role of minuscule representations in algebraic group theory

Abstract

We give a new proof of a theorem by Timmesfeld showing that for simple algebraic groups, abstract modules where all roots act quadratically are direct sums of minuscule representations.