Equations determining the orbit of the highest weight vector in the adjoint representation

2014/01/04 by A. Yu. Luzgarev, Luzgarev, Alexander · 1 citation
Mathematics · #20G05 #20G15 #20G41 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1401.0849

openalex publication_date 2014/01/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We explicitly construct a set of quadratic equations defining the highest weight vector orbit for adjoint representations of Chevalley groups of types D_l, E₆, E₇, and E₈. The combinatorics of these equations is related to the combinatorics of embeddings of the root system of type A₃. We believe that the constructed equations provide a prominent framework for calculations with exceptional groups in adjoint representations, which is particularly interesting for groups of type E₈.

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• Normalizer of the Chevalley group of type E₇

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