The correspondence between the canonical and semicanonical bases

：肖杰（清华大学）
：2023-04-28 15:30
：厦门大学海韵园实验楼105报告厅

报告人：肖杰（清华大学）

时  间：2023年4月28日下午15:30-17:00

地  点：厦门大学海韵园实验楼105报告厅

内容摘要:

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. 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. This is based on a joint work with Jiepeng Fang and Yixin Lan.

个人简介：

肖杰，清华大学数学科学系教授，“新世纪百千万人才工程”入选者，获国家杰出青年基金，教育部跨世纪人才基金。2006年获国家教育部自然科学一等奖。担任国务院学位办学科评议组成员， Chinese Annals of Mathematics、Algebra Colloquium等杂志编委。主要科研方向为代数表示论和量子群，相关研究成果发表于Invent. Math.、Duke Math.、Compositio Math.等国际著名杂志。

 

联系人：阮诗佺