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Locally Quadratic Modules and Minuscule Representations

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Abstract

We give a new, geometric proof of a theorem by Timmesfeld showing that for simple Chevalley groups, abstract modules where all roots act quadratically are direct sums of minuscule representations. Our proof is uniform, treats finite and infinite fields on an equal footing, and includes Lie rings.

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu – Paris Rive Gauche, Université Pierre et Marie Curie, 4, 75005, place Jussieu, France

    Adrien Deloro

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  1. Adrien Deloro
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Correspondence to Adrien Deloro.

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Presented by Michel Brion.

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Deloro, A. Locally Quadratic Modules and Minuscule Representations. Algebr Represent Theor 20, 977–1005 (2017). https://doi.org/10.1007/s10468-017-9671-6

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  • DOI: https://doi.org/10.1007/s10468-017-9671-6

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