论文标题
符号组的组合翻译原理和图表组合学
A combinatorial translation principle and diagram combinatorics for the symplectic group
论文作者
论文摘要
令k为特征p> 2的代数封闭场。我们根据帽子曲线图在不可分解的倾斜模块中计算了不可分解的倾斜模块中的Weyl过滤多数，并在c曲线图上计算了s型组的分解数，假设P比涉及最大分区的最大挂钩长度大。作为推论，我们在相同的假设下获得了Brauer代数的分解数。我们的作品结合了考克斯和德维尔切尔的作品的思想，以及沙利利特的作品与还原群体的代表理论的技术相结合。
Let k be an algebraically closed field of characteristic p>2. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the symplectic group over k in terms of cap-curl diagrams under the assumption that p is bigger than the greatest hook length in the largest partition involved. As a corollary we obtain the decomposition numbers for the Brauer algebra under the same assumptions. Our work combines ideas from work of Cox and De Visscher and work of Shalile with techniques from the representation theory of reductive groups.
