Geometry of certain finite Coxeter group actions

2017/07/11 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.1707.03137

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

Abstract

We determine a fundamental domain for the diagonal action of a finite Coxeter group W on V^{⊕ n}, where V is the reflection representation. This is used to give a stratification of V^{⊕ n}, which is respected by the group action, and we study the geometry, topology and combinatorics of this stratification. These ideas are used to obtain results on the classification of root subsystems up to conjugacy, as well as a character formula for W.

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