Deformed Calogero–Moser Operators and Ideals of Rational Cherednik Algebras

We introduce a class of hyperplane arrangements $$\mathcal {A}$$ in $${\mathbb {C}}^n$$ that generalise the locus configurations Chalykh, Feigin and Veselov. To such an arrangement we associate second order partial differential operator Calogero–Moser type prove this is completely integrable (in sense its centraliser {D}({\mathbb {C}}^n\!\setminus \!\mathcal {A})$$ contains maximal commutative subalgebra Krull dimension n). Our approach based on study shift operators associated ideals spherical Cherednik algebras may be independent interest. Examples include all known deformations with rational potentials. In addition, construct new families examples, including BC-type generalisation deformed Calogero-Moser recently found by Gaiotto Rapčák. describe these examples unified representation-theoretic framework algebras.