Oriented Matroid Structures From Realized Root Systems

2017/10/11 by Matthew Dyer, Weijia Wang, Dyer, Matthew +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1710.04109

openalex publication_date 2017/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the question of uniqueness of the reduced oriented matroid structure arising from root systems of a Coxeter group in real vector spaces. We settle the question for finite Coxeter groups, irreducible affine Weyl groups and all rank three Coxeter groups. In these cases, the oriented matroid structure is unique unless W is of type \widetildeA_n, n≥ 3, in which case there are three possibilities.

Citations

• On rigidity of abstract root systems of Coxeter systems

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