论文标题
含有光滑元素的kazhdan-lusztig右细胞的表征
A characterization of Kazhdan-Lusztig right cells containing smooth elements
论文作者
论文摘要
令$ \ mathfrak {g} $为lie algebra $ \ mathfrak {sl}（n，\ mathbb {c}）$。它的Weyl组是对称组$ s_n $。在本文中，我们要描述一些包含光滑元素的右单元格，这与研究$ \ mathfrak {sl}（n，\ mathbb {c}）$的最高权重模块的相关品种密切相关。首先，我们对仅包含光滑元素的KL右键进行完整的分类。然后，我们通过使用不变子序列和足够条件的KL右单元格给了一个含有一些平滑元素的KL右键，为仅包含非平滑元素的KL右键提供了足够的条件。最后，我们给出有效的算法，以找出给定KL右键中的所有平滑元素。
Let $\mathfrak{g}$ be the Lie algebra $\mathfrak{sl}(n,\mathbb{C})$. Its Weyl group is the symmetric group $S_n$. In this paper, we want to describe some Kazhdan-Lusztig right cells containing smooth elements, which is closely related to the study of associated varieties of highest weight modules of $\mathfrak{sl}(n,\mathbb{C})$. Firstly, we give a complete classification of the KL right cells containing only smooth elements. Then we give a sufficient condition for a KL right cell containing only non-smooth elements by using invariant subsequences and a sufficient condition for a KL right cell containing some smooth elements. Finally, we give an efficient algorithm to find out all the smooth elements in a given KL right cell.
