Hyperplane arrangements associated to symplectic quotient singularities
Hyperplane arrangements associated to symplectic quotient singularities
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DOI：
10.4064/bc116-2
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
G. Bellamy;T. Schedler;U. Thiel
中科院分区：
文献类型：
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作者：
G. Bellamy;T. Schedler;U. Thiel
我们研究了超平面安排，通过最小模型程序，辛商奇点。我们表明，这种超平面的安排等于CM-超平面的安排来自限制理性Cherednik代数的表示理论。我们解释了一些有趣的后果，这种识别的代表性理论的限制合理的Cherednik代数。我们还证明了Calogero-Moser空间是光滑的当且仅当Calogero-Moser族是平凡的。我们描述了CM-超平面的安排与几个特殊的复反射群，其中一些是免费的。
We study the hyperplane arrangements associated, via the minimal model programme, to symplectic quotient singularities. We show that this hyperplane arrangement equals the arrangement of CM-hyperplanes coming from the representation theory of restricted rational Cherednik algebras. We explain some of the interesting consequences of this identification for the representation theory of restricted rational Cherednik algebras. We also show that the Calogero-Moser space is smooth if and only if the Calogero-Moser families are trivial. We describe the arrangements of CM-hyperplanes associated to several exceptional complex reflection groups, some of which are free.