超nabla算子
The super nabla operator
AI总结：
提出具有一般性的super nabla算子，它可导出所有已知的Macdonald本征算子，为该算子族提供统一视角，还得到参数q、t特殊化下的新恒等式并统一组合解释。
摘要：
本文研究了一种名为“super nabla（超nabla）”的新算子，经证明它在修正Macdonald多项式为其联合本征函数的算子中具有一般性。所有已知的Macdonald本征算子都可由super nabla直接得到，包括常用的nabla算子、Delta算子及其他文献中出现的算子。因此，super nabla算子为该算子族提供了统一的整体视角，同时开辟了新的研究方向。我们证明了由这些算子定义中涉及的参数$q$和$t$的特殊化所产生的若干新恒等式，并统一了相关组合解释。
英文摘要：
We consider here a new operator, called ``super nabla'', which is shown to be generic among operators for which the modified Macdonald polynomials are joint eigenfunctions. All previously known Macdonald eigenoperators can readily be obtained from super nabla, including the usual nabla operator, the Delta operators, and other operators that have appeared in the literature. Thus, the super nabla operator furnishes an overall unified viewpoint on this family of operators, as well as opening up new possibilities. We prove several new identities arising from specializations of the parameters $q$ and $t$ involved in the specification of these operators, as well as unifying combinatorial interpretations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
