Projection of root systems

2019/04/03 by Sarah Dijols, Dijols, Sarah
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · #Plant nutrient uptake and metabolism #Microtubule and mitosis dynamics #Aluminum toxicity and tolerance in plants and animals

paper · pdf · doi:10.48550/arxiv.1904.01884

Abstract

Let a be a real euclidean vector space of finite dimension and Σ a root system in a with a basis Δ. Let Θ⊂ Δ and M = M_Θ be a standard Levi of a reductive group G such that a_Θ= a_M / a_G. Let us denote d the dimension of a_Θ, i.e the cardinal of Δ- Θ and Σ_Θ the set of all non-trivial projections of roots in Σ. We obtain conditions on Θ such that Σ_Θ contains a root system of rank d.

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