Cluster additive functions and Ringel’s conjectures
报告题目：Cluster additive functions and Ringel’s conjectures
Let A be a symmetrizable generalized Cartan matrix of size r. A cluster-additive function associated to A is a map from Z times [1,r] to Z satisfying certain mesh type relations. Such functions were introduced by Ringel, which are closely related with additive functions in representation theory. In the case that the Cartan matrix is of finite type, Ringel conjectured that cluster additive functions admit some certain periodicity and any cluster additive function is a non-negative linear combination of cluster-hammock functions, which are a class of “elementary cluster additive functions”.
In this talk, we will give some link between cluster additive functions and cluster algebras. Ringel’s conjectures are easy consequences of our results. This talk is based on a work in progress with Antoine de St. Germain and Prof. Jiang-Hua Lu.