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k-Parabolic Subspace Arrangements

Abstract : In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When k=2, these arrangements correspond to the well-studied Coxeter arrangements. Brieskorn (1971) showed that the fundamental group of the complement of the type W Coxeter arrangement (over $\mathbb{C}$) is isomorphic to the pure Artin group of type W. Khovanov (1996) gave an algebraic description for the fundamental group of the complement of the 3-equal arrangement (over $\mathbb{R}$). We generalize Khovanov's result to obtain an algebraic description of the fundamental group of the complement of the 3-parabolic arrangement for arbitrary finite reflection group. Our description is a real analogue to Brieskorn's description.
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Christopher Severs, Jacob White. k-Parabolic Subspace Arrangements. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.769-780. ⟨hal-01185403⟩

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