论文标题
规范和半义基底座之间的对应关系
The correspondence between the canonical and semicanonical bases
论文作者
论文摘要
鉴于任何对称的cartan基准，卢斯蒂格（Lusztig）提供了一对关键引理，以分别在相应的箭袋上构建不正确的滑轮和在相应的前注射代数上分别构建不可减至的成分的功能。在本文中，我们证明了Lusztig的这两种归纳算法。因此，我们可以定义两个彩色图，并证明它们是异构的。该结果总结了以下陈述：卢斯蒂格（Lusztig）的不可还原组件的函数是包围代数的基础，并直接从卢斯蒂格（Lusztig）卷积的卷积代数内部的半义基础基础来推论晶体结构（在喀什 - 塞塔（Kashiwara-Saito）的意义上）。作为一种应用，我们证明规范基础和半义基础之间的过渡矩阵是上三角形的，所有对角线条目等于1。
Given any symmetric Cartan datum, Lusztig has provided a pair of key lemmas to construct the perverse sheaves over the corresponding quiver and the functions of irreducible components over the corresponding preprojective algebra respectively. In the present article, we prove that these two inductive algorithms of Lusztig coincide. Consequently we can define two colored graphs and prove that they are isomorhic. This result finishes the statement that Lusztig's functions of irreducible components are basis of the enveloping algebra and deduces the crystal structure (in the sense of Kashiwara-Saito) from the semicanonical basis directly inside Lusztig's convolution algebra of the preprojective algebra. As an application, we prove that the transition matrix between the canonical basis and the semicanonical basis is upper triangular with all diagonal entries equal to 1.
