AI 中文总结
该研究类比GLₙ型Macdonald多项式的三类公式，利用分差算子、简约字及两类压缩方法，推导了完全一般性下相对Koornwinder多项式的公式，拓展了Macdonald多项式相关研究。
AI 中文摘要
本文提供了Koornwinder多项式的公式，类似于GLₙ型Macdonald多项式的生成公式、 alcove行走公式和非攻击填充公式。我们用舒伯特演算中使用的分差算子表述生成公式，并利用盒式简约字将alcove行走公式重新表述为未压缩的集合值表格形式。接着，通过两种压缩方式——“绕端压缩”和“跨0间隙压缩”，推导得出基于压缩集合值表格的Koornwinder多项式公式。全文在相对Koornwinder多项式的完全一般性下展开，该多项式是GLₙ情形中所用置换基底Macdonald多项式的类似物。
英文摘要
This paper provides formulas for Koornwinder polynomials in analogy with the creation formula, the alcove walk formula and the non-attacking fillings formula for the type $GL_n$ Macdonald polynomials. We state the creation formula in terms of the divided-difference operators used in Schubert calculus, and we use a box-greedy reduced word to reformulate the alcove walk formula in terms of uncompressed set-valued tableaux. Then two types of compression, ``around-the-end compression'' and ``across-the-$0$-gap compression'', are used to derive a formula for Koornwinder polynomials in terms of compressed set-valued tableaux. Throughout we work in the full generality of relative Koornwinder polynomials, which are the analogues of the permuted basement Macdonald polynomials used in the type $GL_n$ case.
Comments65 pages, 2 appendices
