论文标题
单位群和基本仿射空间的双构基础
Dual canonical bases for unipotent groups and base affine spaces
论文作者
论文摘要
用$ n \ subset sl_k $表示单位上三角矩阵的子组。在本文中，我们表明$ \ mathbb {c} [n] $（和基本仿射空间）的双典型基础可以通过半标准的Young Tableaux参数化。此外，我们使用相应的Semistard Young Tableau的数据在双重规范基础上为每个元素提供一个明确的公式。我们将结果应用于$ \ mathbb {c} [n] $中的群集变量。
Denote by $N \subset SL_k$ the subgroup of unipotent upper triangular matrices. In this paper, we show that the dual canonical basis of $\mathbb{C}[N]$ (and base affine spaces) can be parameterized by semi-standard Young tableaux. Moreover, we give an explicit formula for every element in the the dual canonical basis using the data of the corresponding semistandard Young tableau. We apply our results to study cluster variables in $\mathbb{C}[N]$.
