论文标题
Bigrasdmannian排列和Verma模块
Bigrassmannian permutations and Verma modules
论文作者
论文摘要
我们表明，Bigrastmannian排列决定了$ a $ a $ a $ a $ a $ a $ a $ cokernel的socle。所有这些智能成分都被倒数第二个细胞的Weyl群元素索引。结合起来，由$ w \在S_N $中索引的Verma模块中的Cokernel中的固有成分显示，显示出$ W $的基本集合和分级图片中其学位的确定，以相关的等级功能计算出来。作为应用程序，我们计算了第一个从简单模块到Verma模块的扩展。
We show that bigrassmannian permutations determine the socle of the cokernel of an inclusion of Verma modules in type $A$. All such socular constituents turn out to be indexed by Weyl group elements from the penultimate two-sided cell. Combinatorially, the socular constituents in the cokernel of the inclusion of a Verma module indexed by $w\in S_n$ into the dominant Verma module are shown to be determined by the essential set of $w$ and their degrees in the graded picture are shown to be computable in terms of the associated rank function. As an application, we compute the first extension from a simple module to a Verma module.
