Webs are certain planar diagrams embedded in disks. They index and describe bases of tensor products of representations of $\mathfrak{ sl}_2$ and $\mathfrak{ sl}_3$. There are explicit bijections between webs and certain rectangular tableaux. Work of Petersen-Pylyavskyy-Rhoades (2009) and Russell (2013) shows that these bijections relate web rotation to tableau promotion. We describe the analogous relation between web reflection and tableau evacuation.
Categories: math.CO math.RT