标题： Dunkl和Cherednik算子 显示英文标题

标题： Dunkl and Cherednik operators

摘要： 这篇综述文章是为《数学物理百科全书》第二版撰写的，旨在介绍查尔斯·邓克尔提出的显著算子族，以及伊万·切雷德尼克发现的$q$-类似物。主要重点是这些算子在研究可积多体系统（如卡洛戈罗-莫泽系统和鲁伊斯纳尔斯系统）中的作用。为了将这些构造置于更广泛的背景中，我们指出了它们与有理切雷德尼克代数和双重仿射海克代数理论之间的关系。虽然我们没有包含证明，但提供了原始研究文章的参考文献，并附有简短的历史评论。 显示英文摘要

摘要： This survey article, written for the Encyclopedia of Mathematical Physics, 2nd edition, is devoted to the remarkable family of operators introduced by Charles Dunkl and to their $q$-analogues discovered by Ivan Cherednik. The main focus is on the r\^ole of these operators in studying integrable many-body systems such as the Calogero-Moser and the Ruijsenaars systems. To put these constructions into a wider context, we indicate their relationship with the theory of the rational Cherednik algebras and double affine Hecke algebras. While we do not include proofs, references to the original research articles are provided, accompanied by brief historical comments.