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Flag manifolds over semifields
Algebra & Number Theory ( IF 0.9 ) Pub Date : 2021-11-10 , DOI: 10.2140/ant.2021.15.2037
Huanchen Bao , Xuhua He

In this paper, we develop the theory of flag manifolds over a semifield for any Kac–Moody root datum. We show that a flag manifold over a semifield admits a natural action of the monoid over that semifield associated with the Kac–Moody datum and admits a cellular decomposition. This extends the previous work of Lusztig, Postnikov, Rietsch, and others on the totally nonnegative flag manifolds (of finite type) and the work of Lusztig, Speyer, Williams on the tropical flag manifolds (of finite type). As an important consequence, we prove a conjecture of Lusztig on the duality of a totally nonnegative flag manifold of finite type.



中文翻译:

在半场上标记流形

在本文中,我们为任何 Kac-Moody 根数据开发了半场上的标志流形理论。我们表明,半域上的标志流形允许幺半群在与 Kac-Moody 数据相关的半域上的自然作用,并允许元胞分解。这扩展了 Lusztig、Postnikov、Rietsch 和其他人在完全非负标志流形(有限类型)上的工作以及 Lusztig、Speyer、Williams 在热带标志流形(有限类型)上的工作。作为一个重要的结果,我们证明了 Lusztig 关于有限类型的完全非负标志流形的对偶性的猜想。

更新日期:2021-11-10
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