发表机构
National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了Lusztig与Kashiwara构造的量子群典范基的各类分拆重合，据此得出开Richardson簇对应子集与Schubert胞腔对应子集的交集关系，并证明A型中开Richardson簇的权在对应Bruhat区间多面体中饱和。
AI 中文摘要
我们证明了由Lusztig和Kashiwara构造的量子群典范基的各类分拆是重合的。利用该分拆，我们证明了对应于开Richardson簇的子集等于对应于Schubert胞腔的子集的交集。我们还证明了在A型中，来自开Richardson簇的权在对应的Bruhat区间多面体中是饱和的。
英文摘要
We show that various partitions of the canonical basis of quantum groups constructed by Lusztig and by Kashiwara coincide. Using this partition, we show that the subset corresponding to open Richardson varieties equals to the intersection of the subsets corresponding to the Schubert cells. We also show that in type $A$, the weights from open Richardson varieties are saturated in the corresponding Bruhat interval polytope.
CommentsMinor updates on references, 14 pages
