TABLEAU EVACUATION AND WEBS

Abstract

Webs are certain planar diagrams embedded in disks. They index and describe bases of tensor products of representations of sl2 and sl3. 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.