Tableau evacuation and webs
Rebecca Patrias, Oliver Pechenik

TL;DR
This paper explores the relationship between web symmetries and tableau operations, specifically connecting web reflection to tableau evacuation, extending known bijections between webs and tableaux.
Contribution
It introduces the correspondence between web reflection and tableau evacuation, expanding the understanding of web-tableau symmetries beyond rotation and promotion.
Findings
Web reflection corresponds to tableau evacuation.
Bijections relate web symmetries to tableau operations.
Extends previous work on web rotation and promotion.
Abstract
Webs are certain planar diagrams embedded in disks. They index and describe bases of tensor products of representations of and . 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Topics in Algebra
