Simple-root bases for Shi arrangements
Simple-root bases for Shi arrangements
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DOI：
10.1016/j.jalgebra.2014.09.011
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发表时间：
2011-11
影响因子：
0.9
通讯作者：
T. Abe;H. Terao
中科院分区：
文献类型：
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作者：
T. Abe;H. Terao
在对Edelman-Reiner猜想的肯定回答中，Yoshinaga证明了扩展的SHI排列的锥的对数导子模是自由模。然而，除了基地的存在，我们对基地本身知之甚少。在这篇文章中，我们证明了两个不同的基的唯一存在性，我们称之为单根基加(SRB+)和单根基减(SRB−)。相对于单根，它们具有良好的可除性。
In his affirmative answer to the Edelman–Reiner conjecture, Yoshinaga proved that the logarithmic derivation modules of the cones of the extended Shi arrangements are free modules. However, we know very little about the bases themselves except their existence. In this article, we prove the unique existence of two distinguished bases which we call the simple-root basis plus (SRB+) and the simple-root basis minus (SRB−). They are characterized by nice divisibility properties relative to the simple roots.