AI 中文总结
本文在t=1的情况下，通过对Kostka系数K_{ΩΛ}(q,1)给出基于m-分拆Ω对应图标准填充的组合解释，证明了原始Macdonald正性猜想向m-对称领域的扩展。
AI 中文摘要
我们在t=1的情况下，证明了原始Macdonald正性猜想向m-对称领域的扩展。该证明通过对Kostka系数K_{ΩΛ}(q,1)进行组合解释实现，此解释基于与m-分拆Ω相关联的图的标准填充，它推广了通常Macdonald情形下由标准表格的主指标统计给出的解释。
英文摘要
We prove, in the case $t=1$, the extension to the $m$-symmetric world of the original Macdonald positivity conjecture. This is achieved by giving a combinatorial interpretation of the Kostka coefficients $K_{ΩΛ}(q,1)$ in terms of standard fillings of the diagram associated to the $m$-partition $Ω$. This interpretation generalizes the one in the usual Macdonald case, which is given by a major index statistic on standard tableaux.
Comments20 pages, 2 figures
