Tableau evacuation and webs

Abstract

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.

10 pages, exposition improved thanks to helpful feedback

References in corpus (2)

• Promotion of Kreweras words
• A web basis of invariant polynomials from noncrossing partitions

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• Order polynomial product formulas and poset dynamics
• Twists, Higher Dimer Covers, and Web Duality for Grassmannian Cluster Algebras
• Web invariants for flamingo Specht modules