Orbits of vectors in some representations. II

2021/12/11 by Pevzner, Igor
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2112.06077

Abstract

Let Φ be a root system of type A_l or D_l. Let K be a field of characteristic not 2. Let δ be the maximal root of Φ and set Φ₀ = \α∈Φ; δ⊥α\. We describe orbits of the group G_{\rm sc}(Φ₀, K) acting on the set ⟨ e_α; ∠(α, δ) = π/3⟩.

Related

• Orbits of vectors in some representations. III
• On counting orbits in root systems
• The action of a Coxeter element on an affine root system
• Root systems, symmetries and linear representations of Artin groups
• The B-orbits on a Hermitian symmetric variety in characteristic 2