2000/10/31 by David Bessis · 63 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Braid #Braid group #Braid theory #Combinatorics #Discrete mathematics #Geometric and Algebraic Topology #Invariant (physics) #Mathematics #Pure mathematics #math.AT #math.GR #msc:20F36
paper · pdf · doi:10.1007/s002220100155
published in Inventiones mathematicae 145(3), 487-507 (Springer Science+Business Media) · 21 pages
arxiv created 2001/01/17 · openalex publication_date 2001/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Broué-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is invariant-theoretic and does not use the classification. The two ingredients are Springer theory of regular elements and a Zariski-like theorem.