Regular cell complexes in total positivity
Regular cell complexes in total positivity
复制标题
常规细胞复合体总体呈阳性
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
P. Hersh
中科院分区：
文献类型：
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作者：
P. Hersh
Fomin 和 Shapiro 推测，在 ${mathbb{R}}$ 上定义并分裂的半单单连通代数群中，Borel 子群的单能根的完全非负实部的 Bruhat 分层中的恒等联是与球同胚的正则 CW 复数。本文的主要结果就是证明了这个猜想。这就完成了 Bernstein 问题的解决方案，即识别由具有 Bruhat 阶的（较低）区间作为闭合偏集的表示论自然产生的正则 CW 复合体。一个关键因素是确定有限 CW 复形对于特征图的选择是否规则的新标准；它最自然地适用于来自常规 CW 复合体的映射图像，并且基于闭包偏序集与余维一拓扑的组合数学的相互作用。
Fomin and Shapiro conjectured that the link of the identity in the Bruhat stratification of the totally nonnegative real part of the unipotent radical of a Borel subgroup in a semisimple, simply connected algebraic group defined and split over ${mathbb{R}}$ is a regular CW complex homeomorphic to a ball. The main result of this paper is a proof of this conjecture. This completes the solution of the question of Bernstein of identifying regular CW complexes arising naturally from representation theory having the (lower) intervals of Bruhat order as their closure posets. A key ingredient is a new criterion for determining whether a finite CW complex is regular with respect to a choice of characteristic maps; it most naturally applies to images of maps from regular CW complexes and is based on an interplay of combinatorics of the closure poset with codimension one topology.