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摘要翻译：
本文研究了有理Cherednik代数$H_\kappa=H_\kappa({\mathbb Z}_l={\mathbb Z}_l)$对循环群${\mathbb Z}_l/l{\mathbb Z}$的表示理论及其与$A_{l-1}^{（1）}$型颤簇$M_\theta(\delta)$的几何关系。考虑了具有不同参数的$H_\kappa$-模范畴之间的一个函子，称为移位函子，并给出了它是范畴等价的条件。我们还考虑了从具有良好过滤的$H_\kappa$-模范畴到$M_\theta(\delta)$上的相干束范畴的一个函子。证明了该函子对$H_\kappa$的正则表示的象是$M_\theta(\delta)$上的重言丛。作为推论，我们确定了标准模的特征圈。对[Gordon,arxiv:Math/0703150v1]中的一个猜想在${\mathbb Z}_l$的情况下给出了肯定的回答。
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英文标题：
《Characteristic cycles of standard modules for the rational Cherednik
algebra of type Z/lZ》
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作者：
Toshiro Kuwabara
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We study the representation theory of the rational Cherednik algebra $H_\kappa = H_\kappa({\mathbb Z}_l)$ for the cyclic group ${\mathbb Z}_l = {\mathbb Z} / l {\mathbb Z}$ and its connection with the geometry of the quiver variety $M_\theta(\delta)$ of type $A_{l-1}^{(1)}$. We consider a functor between the categories of $H_\kappa$-modules with different parameters, called the shift functor, and give the condition when it is an equivalence of categories. We also consider a functor from the category of $H_\kappa$-modules with good filtration to the category of coherent sheaves on $M_\theta(\delta)$. We prove that the image of the regular representation of $H_\kappa$ by this functor is the tautological bundle on $M_\theta(\delta)$. As a corollary, we determine the characteristic cycles of the standard modules. It gives an affirmative answer to a conjecture given in [Gordon, arXiv:math/0703150v1] in the case of ${\mathbb Z}_l$.
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PDF链接：
https://arxiv.org/pdf/0801.4136
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