论文标题
右单元中舒伯特品种的奇异性
Singularities of Schubert Varieties within a Right Cell
论文作者
论文摘要
我们描述了一种算法，该算法在woo-yong的意义上嵌入了对称组的任何bruhat间隔中的任何bruhat间隔，该间隔中极端位于相同的右kazhdan-lusztig细胞中。这个显然无害的事实在查找$ \ mathfrak {sl} _n $的可简化相关品种的示例中有应用，其中最高的重量模块以及对对称组的$ W $ graphs的研究，以及比较对称组或其Hecke Hecke algebra algebra的各种基础。例如，我们能够系统地为1980年代Borho-Brylinski和Joseph的问题提供许多负面答案，威廉姆森仅在2014年才通过计算机计算解决。
We describe an algorithm which pattern embeds, in the sense of Woo-Yong, any Bruhat interval of a symmetric group into an interval whose extremes lie in the same right Kazhdan-Lusztig cell. This apparently harmless fact has applications in finding examples of reducible associated varieties of $\mathfrak{sl}_n$-highest weight modules, as well as in the study of $W$-graphs for symmetric groups, and in comparing various bases of irreducible representations of the symmetric group or its Hecke algebra. For example, we are able to systematically produce many negative answers to a question from the 1980s of Borho-Brylinski and Joseph, which had been settled by Williamson via computer calculations only in 2014.
