论文标题
国旗品种的扭曲产物中的总阳性
Total positivity in twisted product of flag varieties
论文作者
论文摘要
我们表明，Kac-Moody组的Flag品种扭曲产物的完全非负部分接受了细胞分解，并且每个细胞的闭合是具有边界的拓扑歧管。我们还建立了每个完全阳性细胞的明确参数化。 在双旗品种和辫子品种的特殊情况下，我们表明，完全非负零件是常规的CW综合体对封闭球的同型。此外，我们证明，还原组中任何完全非负双bruhat细胞的链接是与封闭球的常规CW复合物同态同质形态，解决了Fomin和Zelevinsky的开放问题。
We show that the totally nonnegative part of the twisted product of flag varieties of a Kac-Moody group admits a cellular decomposition, and the closure of each cell is a topological manifold with boundary. We also establish explicit parameterizations of each totally positive cell. In the special cases of double flag varieties and braid varieties, we show that the totally nonnegative parts are regular CW complexes homeomorphic to closed balls. Moreover, we prove that the link of any totally nonnegative double Bruhat cell in a reductive group is a regular CW complex homeomorphic to a closed ball, solving an open problem of Fomin and Zelevinsky.
