On the Grassmannian root conjecture
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题 目：On the Grassmannian root conjecture
报告人: Bernhard Keller (巴黎西岱大学)
时 间: 2023年1月10日 周二上午10:00-11:00
地 点: 西大楼108报告厅
摘 要：In 2016, Jensen-King-Su introduced an (infinite-dimensional, noncommutative) Gorenstein algebra whose category of Cohen-Macaulay modules categorifies the cluster structure on the Grassmannian of k-dimensional subspaces in n-dimensional space. Among other results, they obtained a map taking each cluster monomial to an element of the root lattice of the tree Jk,n with three branches of lengths 2, k and n-k. They conjectured that the images of the cluster variables are roots and checked this for the cases where Jk,n is a Dynkin diagram. Baur-Bogdanic-Garcia Elsener-Li confirmed the conjecture in many other examples in 2020. In this talk, we will provide further numerical evidence for the conjecture and use tilting theory to establish a representation-theoretic link between the category of Cohen-Macaulay modules and the representations of suitable quivers with underlying graph Jk,n.