Normal Reflection Subgroups

2020/06/11 by Carlos E. Arreche, Nathan Williams, Arreche, Carlos E. +1
Mathematics · #05E10 #20F55 #Advanced Operator Algebra Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2006.06575

openalex publication_date 2020/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study normal reflection subgroups of complex reflection groups. Our point of view leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a product of linear factors involving generalized exponents. Our refinement gives a uniform proof and generalization of a recent theorem of the second author.

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