Parabolic subgroup orbits on finite root systems

2017/08/02 by Matthew Dyer, Dyer, M. J., G Lehrer +1
Mathematics · #17B22 (Secondary) #20F55 (Primary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1708.00913

openalex publication_date 2017/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Oshima's Lemma describes the orbits of parabolic subgroups of irreducible finite Weyl groups on crystallographic root systems. This note generalises that result to all root systems of finite Coxeter groups, and provides a self contained proof, independent of the representation theory of semisimple complex Lie algebras.

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