Mathematical Physics
[Submitted on 7 Nov 2023
]
Title: Baxter $Q$-operator for the hyperbolic Calogero--Moser system
Title: Baxter $Q$算子对于双曲 Calogero--Moser 系统
Abstract: We introduce a $Q$-operator $\mathcal{Q}_z$ for the hyperbolic Calogero--Moser system as a one-parameter family of explicit integral operators. We establish the standard properties of a $Q$-operator, i.e.~invariance of Hamiltonians, commutativity for different parameter values and that its eigenvalues satisfy an explicitly given first order ordinary difference equation in the parameter $z$.
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