论文标题
完全非负旗品种的产品结构和规律定理
Product structure and regularity theorem for totally nonnegative flag varieties
论文作者
论文摘要
Lusztig引入了完全非负标志品种。它具有丰富的组合，几何和谎言理论结构。在本文中，我们在任意Kac-Moody群体的完整旗帜上引入了（新的）$ J $ - 总计阳性，从而推广了（普通）总阳性。 我们表明，$ j $的非负标志品种将细胞分解为完全阳性的$ j $ -Richardson品种。此外，每个完全积极的$ J $ -Richardson Variety都承认了一个有利的分解，称为产品结构。再加上广义的庞加雷猜想，我们证明，每个完全正面的$ j $ -richardson品种的关闭是封闭球的常规CW复合物同构。此外，完整标志上的$ J $ - 总数积极性为（普通）完全非负部分标志品种提供了模型。结果，我们证明，每个（普通）完全正面理查森品种的封闭是一个常规的CW复合物同质形态，可以证实Galashin，Karp和Lam的猜想。
The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this paper, we introduce a (new) $J$-total positivity on the full flag variety of an arbitrary Kac-Moody group, generalizing the (ordinary) total positivity. We show that the $J$-totally nonnegative flag variety has a cellular decomposition into totally positive $J$-Richardson varieties. Moreover, each totally positive $J$-Richardson variety admits a favorable decomposition, called a product structure. Combined with the generalized Poincare conjecture, we prove that the closure of each totally positive $J$-Richardson variety is a regular CW complex homeomorphic to a closed ball. Moreover, the $J$-total positivity on the full flag provides a model for the (ordinary) totally nonnegative partial flag variety. As a consequence, we prove that the closure of each (ordinary) totally positive Richardson variety is a regular CW complex homeomorphic to a closed ball, confirming conjectures of Galashin, Karp and Lam.
