论文标题
量规和积分转换产生的Van Diejen模型的本征函数
Eigenfunctions of the van Diejen model generated by gauge and integral transformations
论文作者
论文摘要
我们介绍了如何使用范围和积分变换来构建$ bc_ {m} $相对论Calogero-Moser-Sutherland模型的主要哈密顿的特征函数。特别是，我们发现某些$ bc $ type椭圆形超几何积分，包括I型和II型的椭圆形Selberg积分，在某些参数限制下作为Van Diejen模型的特征函数出现。其中还包括所谓的Van Diejen操作员模块化对的联合征函数。此外，这些转换与作用于模型参数空间的$ e_ {8} $ Weyl组的反射有关。
We present how explicit eigenfunctions of the principal Hamiltonian for the $BC_{m}$ relativistic Calogero-Moser-Sutherland model, due to van Diejen, can be constructed using gauge and integral transformations. In particular, we find that certain $BC$-type elliptic hypergeometric integrals, including elliptic Selberg integrals, of both Type I and Type II arise as eigenfunctions of the van Diejen model under some parameter restrictions. Among these are also joint eigenfunctions of so-called modular pairs of van Diejen operators. Furthermore, these transformations are related to reflections of the $E_{8}$ Weyl group acting on the space of model parameters.
