Cluster Structures on Braid VarietiesStudent-Run Research Seminar
|Tonie Scroggin, UC Davis
|1147 Mathematical Science Building
|Wed, Oct 4 2023, 12:10PM
Given a simple algebraic group $G$ and an element $\beta$ of the positive braid monoid, we consider an affine, smooth algebraic variety $X(\beta)$ which includes well known varieties in Lie theory such as open Richardson and positroid varieties. In this talk we will show that the coordinate ring of regular functions of any braid variety is a cluster algebra using Lusztig cycles in algebraic weaves.