On exchange matrices from string diagrams

讲座时间 Datetime: 2022年6月6日，星期一，16:00-17:30

地点 Venue: 腾讯线上会议：946-628-9201

 主持人 Host：黄敏

报告人 Speaker：曹培根

单位 Affiliation：希伯来大学

报告摘要 Abstract：

Inspired by Fock-Goncharov's amalgamation procedure, Shen-Weng introduced string diagrams, which are very useful to describe many interesting skew-symmetrizable matrices closely related with Lie theory.  We prove that the skew-symmetrizable matrices from string diagrams are in the smallest class of skew-symmetrizable matrices containing the 1×1 zero matrix and closed under mutations and source-sink extensions. This result applies to the exchange matrices of cluster algebras from double Bruhat cells, unipotent cells, double Bott-Samelson cells and so on. Our main result can be used to explain why many skew-symmetrizable matrices from Lie theory have reddening sequences. It can be also used to prove some interesting results regarding non-degenerate potentials on many quivers from Lie theory.