论文标题
部分标志品种的坐标环上的簇结构
A cluster structure on the coordinate ring of partial flag varieties
论文作者
论文摘要
本文的主要目的是表明，部分标志品种$ \ mathbb {c} [g / p_k^{ - }] $（如果$ g $是任何简单相关的半粘附的半粘合式综合体组）的（g / p_k^{ - }）的（多均匀的）坐标环。我们使用派生属性和特殊举起图来证明坐标环$ \ Mathcal {a} $的坐标环$ \ Mathbb {c} [c} [n_k] [n_k] $由GoodeArl和Yakimov构建的Schubert Cell构建的schubert cell和Yakimov构建的Yakimov构建，以明确的方式，以a cluster结构$ \ hat $ \ hat nirive $ \ hat niring a c c ccc {相应的部分标志品种。然后，我们使用最小的条件来证明群集代数$ \ hat {\ mathcal {a}} $的确等于$ \ mathbb {c} [g / p_k^{ - }] $。
The main goal of this paper is to show that the (multi-homogeneous) coordinate ring of a partial flag variety $\mathbb{C} [G / P_K^{-}]$ admits a cluster algebra structure if $G$ is any simply-connected semisimple complex algebraic group. We use derivation properties and a special lifting map to prove that the cluster algebra structure $\mathcal{A}$ of the coordinate ring $\mathbb{C}[N_K]$ of a Schubert cell constructed by Goodearl and Yakimov can be lifted, in an explicit way, to a cluster structure $\hat{\mathcal{A}}$ living in the coordinate ring of the corresponding partial flag variety. Then we use a minimality condition to prove that the cluster algebra $\hat{\mathcal{A}}$ is indeed equal to $\mathbb{C}[G / P_K^{-}]$.
