标题： 广义Calogero模型中的Dunkl辛代数 显示英文标题

标题： Dunkl symplectic algebra in generalized Calogero models

摘要： 我们研究了使用Dunkl算子变形的辛sp(2N)代数的性质，该代数描述了广义N粒子量子Calogero模型的动力对称性。 它包含由变形的酉生成元形成的对称子代数以及（非变形的）sl(2,R)共形子代数。 推导出了变形的辛生成元之间的显式关系。 基于共形自旋和Dunkl角动量代数的Casimir元素之间的匹配，标准和广义Calogero模型的独立波函数，用变形的球谐函数表示，根据无限维最低态sl(2,R)多重态进行分类。 同时，(广义)Calogero-Moser模型的任何多项式运动积分生成一个有限维最高态共形多重态，其后代通过量子场论中的Weyl有序乘积表示。 显示英文摘要

摘要： We study the properties of the symplectic sp(2N) algebra deformed using Dunkl operators, which describe the dynamical symmetry of the generalized N-particle quantum Calogero model. It contains a symmetry subalgebra formed by the deformed unitary generators as well as the (nondeformed) sl(2,R) conformal subalgebra. An explicit relation among the deformed symplectic generators is derived. Based on the matching between the Casimir elements of the conformal spin and Dunkl angular momentum algebras, the independent wavefunctions of the both the standard and generalized Calogero models, expressed in terms of the deformed spherical harmonics, are classified according to infinite-dimensional lowest-state sl(2,R) multiplets. Meanwhile, any polynomial integral of motion of the (generalized) Calogero-Moser model generates a finite-dimensional highest-state conformal multiplet with descendants expressed via the Weyl-ordered product in quantum field theory.