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Reducibility of finite reflection groups

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Abstract

A finite (pseudo-)reflection group G naturally gives rise to a hyperplane arrangement, i.e., its reflection arrangement. We show that G is reducible if and only if its reflection arrangement is reducible.

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References

  1. Serre J P. Linear Representations of Finite Groups. New York: Springer-Verlag, 1977

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  2. Orlk P, Terao H. Arrangements of Hyperplanes. Berlin: Springer-Verlag, 1992

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Authors and Affiliations

  1. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    JianMing Yu

  2. Department of Mathematics and Information Science, Faculty of Sciences, Beijing University of Chemical Technology, Beijing, 100029, China

    GuangFeng Jiang

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  1. JianMing Yu
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  2. GuangFeng Jiang
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Correspondence to JianMing Yu.

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Yu, J., Jiang, G. Reducibility of finite reflection groups. Sci. China Math. 55, 947–948 (2012). https://doi.org/10.1007/s11425-011-4341-3

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  • DOI: https://doi.org/10.1007/s11425-011-4341-3

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