JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (2): 66-70.doi: 10.6040/j.issn.1671-9352.0.2018.127

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Simple-root bases for the deformations of extended Shi arrangements

GAO Rui-mei1, GAO Jia-ying2, CHU Ying1*   

  1. 1. School of Science, Changchun University of Science and Technology, Changchun 130022, Jilin, China;
    2. School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, Jilin, China
  • Published:2019-02-25

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Abstract: The cone of an extended Shi arrangement is used S k to denote. The existence of the simple-root bases of the derivation modules for S k and the freeness of B +Γ and B -Γ are proved. They are formed by adding and deleting some reflection hyperplanes of S k, which are corresponding to simple roots. B +Γ and B -Γ are called the deformations of extended Shi arrangements. According to Saitos criterion, the explicit constructions of the bases of the derivation modules are given for B +Γ and B -Γ, and the exponents of them are calculated.

Key words: Shi arrangement, simple-root basis, free arrangement, derivation module

CLC Number: 

  • O189
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