Deformed Calogero-Moser Operators and Ideals of Rational Cherednik Algebras
Deformed Calogero-Moser Operators and Ideals of Rational Cherednik Algebras
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变形的Calogero-Moser算子和有理Cherednik代数的理想
DOI：
10.1007/s00220-022-04595-4
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发表时间：
2022
影响因子：
2.4
通讯作者：
Berest Y
中科院分区：
文献类型：
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作者：
Berest Y
我们引入了一类超平面排列，概括了 Chalykh、Feigin 和 Veselov 的轨迹配置。对于这样的安排，我们将 Calogero-Moser 类型的二阶偏微分算子关联起来，并证明该算子是完全可积的（从某种意义上说，它的中心化器不包含 Krull 维数 n 的最大交换子代数）。我们的方法基于对可能具有独立兴趣的球切雷德尼克代数中的移位算子和相关理想的研究。例子包括所有已知的具有有理势的 Calogero-Moser 算子的完全可积变形。此外，我们构建了新的示例族，包括 Gaiotto 和 Rapčák 最近发现的变形 Calogero-Moser 算子的 BC 型推广。我们在有理切雷德尼克代数的统一表示理论框架中描述这些例子。
We introduce a class of hyperplane arrangementsinthat generalise the locus configurations of Chalykh, Feigin and Veselov. 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 incontains a maximal commutative subalgebra of Krull dimensionn). Our approach is based on the study of shift operators and associated ideals in spherical Cherednik algebras that may be of independent interest. Examples include all known completely integrable deformations of Calogero–Moser operators with rational potentials. In addition, we construct new families of examples, including a BC-type generalisation of the deformed Calogero-Moser operators recently found by Gaiotto and Rapčák. We describe these examples in a unified representation-theoretic framework of rational Cherednik algebras.