论文标题
变形的Calogero- Moser操作员和理性的Cherednik代数的理想
Deformed Calogero--Moser operators and ideals of rational Cherednik algebras
论文作者
论文摘要
我们考虑了一类超平面布置$ \ mathcal a $ in $ {\ mathbb c}^n $，将\ cite {cfv}的基因座配置推广。 To such an arrangement we associate a second order partial differential operator of Calogero-Moser type, and prove that this operator is completely integrable (in the sense that its centraliser in $\mathcal{D}({\mathbb C}^n\setminus\mathcal A)$ contains a maximal commutative subalgebra of Krull dimension $n$).我们的方法基于对可能具有独立关注的球形Cherednik代数中的转移操作员和相关理想的研究。这些示例包括出现在文献中的所有已知（理性）Calogero-Moser系统的家庭；我们还构建了一些新示例，包括D. Gaiotto和M.Rapčák最近在\ cite {gr}中发现的完全集成运营商的BC型类似物。我们将这些示例描述为在精神上与\ cite {beg}和\ cite {bc}的一般框架的一般框架。
We consider a class of hyperplane arrangements $\mathcal A$ in ${\mathbb C}^n$ that generalise the locus configurations of \cite{CFV}. To such an arrangement we associate a second order partial differential operator of Calogero-Moser type, and prove that this operator is completely integrable (in the sense that its centraliser in $\mathcal{D}({\mathbb C}^n\setminus\mathcal A)$ contains a maximal commutative subalgebra of Krull dimension $n$). Our approach is based on the study of shift operators and associated ideals in the spherical Cherednik algebra that may be of independent interest. The examples include all known families of deformed (rational) Calogero-Moser systems that appeared in the literature; we also construct some new examples, including a BC-type analogues of completely integrable operators recently found by D. Gaiotto and M. Rapčák in \cite{GR}. We describe these examples in a general framework of rational Cherednik algebras close in spirit to \cite{BEG} and \cite{BC}.
