Restricted rational Cherednik algebras
Restricted rational Cherednik algebras
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DOI：
10.4171/171-1/24
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发表时间：
2016-03
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影响因子：
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通讯作者：
U. Thiel
中科院分区：
文献类型：
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作者：
U. Thiel
本文综述了限制有理Cherednik代数的表示理论。这些是t=0时有理Cherednik代数的有限维商。他们的表示理论与卡洛杰罗-莫泽空间的几何结构有关，而且有很多证据表明，他们包含了赫克代数的某些信息，尽管确切的联系到目前为止还不清楚。我们概述了基本理论以及一些开放的问题和猜想，并在循环和二面体情况下给出了明确的结果。
We give an overview of the representation theory of restricted rational Cherednik algebras. These are certain finite-dimensional quotients of rational Cherednik algebras at t=0. Their representation theory is connected to the geometry of the Calogero-Moser space, and there is a lot of evidence that they contain certain information about Hecke algebras even though the precise connection is so far unclear. We outline the basic theory along with some open problems and conjectures, and give explicit results in the cyclic and dihedral cases.