Stable hyperplane arrangements

2025/10/13 by Oshima, Toshio
#52C35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.11099

Abstract

We classify complex hyperplane arrangements \mathcal A whose intersection posets L(\mathcal A) satisfy L(\mathcal A)=π_i^-1∘π_i(L(\mathcal A)) for i=1,…,n. Here π_i denotes the projection from \mathbb Cⁿ onto \mathbb C^n-1 defined by that forgets the coordinate x_i of (x₁,…,x_n)∈\mathbb Cⁿ, and π_i(L(\mathcal A))=\π_i(S)| S∈ L(\mathcal A)\. We show that such arrangements \mathcal A arise as pullbacks of the mirror hyperplanes of complex reflection groups of type A or B.

Citations

• Middle convolutions of KZ-type equations and single-elimination tournaments

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