2008/09/02 by Iván Marín, Marin, Ivan · 1 citation
Engineering · Mathematics · #15A63 #20C15 #20F55 #52C35 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.0809.0384
openalex publication_date 2008/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
After having established elementary results on the relationship between a finite complex (pseudo-)reflection group W < GL(V) and its reflection arrangement A, we prove that the action of W on A is canonically related with other natural representations of W, through a `periodic' family of representations of its braid group. We also prove that, when W is irreducible, then the squares of defining linear forms for A span the quadratic forms on V, which imply |A| >= n(n+1)/2 for n = dim V, and relate the W-equivariance of the corresponding map with the period of our family.