The modality of a Borel subgroup in a simple algebraic group of type E₈

2018/02/09 by Simon M. Goodwin, Peter Mosch, Goodwin, Simon +3
Mathematics · #14L24 #20G1 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1802.03175

openalex publication_date 2018/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 mod(B:\mathfrak u) = 20, when G is of type \mathrm E₈. This completes the determination of the values for mod(B:\mathfrak u) for G of exceptional type.

Citations

• On Higman's k(U_n(\mathbbF_q)) conjecture
• ON THE COADJOINT ORBITS OF MAXIMAL UNIPOTENT SUBGROUPS OF REDUCTIVE GROUPS

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