Kazhdan-Lusztig left cell preorder and dominance order

Zhekun He, Jun Hu, Yujiao Sun

Let "${\le }_L$" be the Kazhdan-Lusztig left cell preorder on the symmetric group $S_n$. Let $w\mapsto (P(w),Q(w))$ be the Robinson-Schensted-Knuth correspondence between $S_n$ and t…