On the Grassmannian root conjecture
par
Amphi Jordan
Bat. Braconnier
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 with three branches of lengths k, n-k and 2. They conjectured that the images of the cluster variables are roots and checked this for the cases where J_{k,n} is a Dynkin diagram. Baur–Bogdanić–García Elsener and Baur–Bogdanić–García Elsener–Li (preprint) confirmed the conjecture in many other cases in 2020. In this largely expository talk, we will provide further evidence for the conjecture. This is a report on ongoing joint work with Sarjick Bakshi, Mingfa Chen and Haoyu Wang.
Alexander Thomas