The Modality of a Borel Subgroup in a Simple Algebraic Group of Type E₈

ABSTRACT

Let G be a simple algebraic group over an algebraically closed field k, where char k is either 0 or a good prime for G. We consider the modality $\mathrm{mod}(B:\mathfrak{u})$ of the action of a Borel subgroup B of G on the Lie algebra $\mathfrak{u}$ of the unipotent radical of B, and report on computer calculations used to show that $\mathrm{mod}(B:\mathfrak{u})=20$, when G is of type E₈. This completes the determination of the values for $\mathrm{mod}(B:\mathfrak{u})$ for G of exceptional type.

KEYWORDS:

• Borel subgroups
• modality
• reductive algebraic groups

MATHEMATICS SUBJECT CLASSIFICATION:

• 20G40, 20E45