论文标题
完全非负的热带旗帜和完全非负旗裙
Totally Nonnegative Tropical Flags and the Totally Nonnegative Flag Dressian
论文作者
论文摘要
我们研究了完整标志品种及其热带化的完全非负部分。我们表明，Lusztig的非负完整标志品种的概念与具有非负pl {ü} cker坐标的完整标志品种中的标志一致。这反映了完全非负史拉尼亚人的特征，就像帕尔曼尼亚人的那些点，其pl {ü} cker坐标都是无负的。然后，我们研究热带完整的国旗品种和完整的旗帜装饰台，它们是完整标志品种的两个热带版本，分别捕获了热带线性空间的可实现和抽象的标志。通常，完整的Flag Dressian正确包含热带完整的旗帜品种。但是，我们表明这些空间的完全非负部分重合。
We study the totally nonnegative part of the complete flag variety and of its tropicalization. We show that Lusztig's notion of nonnegative complete flag variety coincides with the flags in the complete flag variety which have nonnegative Pl{ü}cker coordinates. This mirrors the characterization of the totally nonnegative Grassmannian as those points in the Grassmannian whose Pl{ü}cker coordinates are all nonnegative. We then study the tropical complete flag variety and complete flag Dressian, which are two tropical versions of the complete flag variety, capturing realizable and abstract flags of tropical linear spaces, respectively. In general, the complete flag Dressian properly contains the tropical complete flag variety. However, we show that the totally nonnegative parts of these spaces coincide.
