Bispectrality for the quantum Ruijsenaars model and its integrable deformation
Bispectrality for the quantum Ruijsenaars model and its integrable deformation
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量子 Ruijsenaars 模型的双谱性及其可积变形
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
O. Chalykh
中科院分区：
文献类型：
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作者：
O. Chalykh
提出了具有整数耦合参数的量子有理 Ruijsenaars 模型本征函数的基本构造。作为副产品，我们在该模型和三角 Calogero-Moser 模型之间建立了双谱对偶性。特别是，这为计算 Jack 多项式提供了一种新方法。我们还提出了 Ruijsenaars 模型的某种单参数变形，证明了其可积性和双谱性。考虑了麦克唐纳与其他根系统和差分算子相关的概括。
An elementary construction of the eigenfunctions for the quantum rational Ruijsenaars model with integer coupling parameter is presented. As a by-product, we establish the bispectral duality between this model and the trigonometric Calogero–Moser model. In particular, this gives a new way for calculating Jack polynomials. We propose also a certain one-parameter deformation of the Ruijsenaars model, proving its integrability and bispectrality. The generalizations related to other root systems and difference operators by Macdonald are considered.