2024/04/16 by Ayah Almousa, Almousa, Ayah, Victor Reiner +3 · 1 citation
Mathematics · #05B35 #16S37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2404.10858
openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Supersolvable hyperplane arrangements and matroids are known to give rise to certain Koszul algebras, namely their Orlik-Solomon algebras and graded Varchenko-Gel'fand algebras. We explore how this interacts with group actions, particularly for the braid arrangement and the action of the symmetric group, where the Hilbert functions of the algebras and their Koszul duals are given by Stirling numbers of the first and second kinds, respectively. The corresponding symmetric group representations exhibit branching rules that interpret Stirling number recurrences, which are shown to apply to all supersolvable arrangements. They also enjoy representation stability properties that follow from Koszul duality.