Tableau evacuation and webs-Reference-Cited by-同舟云学术

Tableau evacuation and webs

Published:2023-09-29 Issue:30 Volume:10 Page:341-352
ISSN:2330-1511
Container-title:Proceedings of the American Mathematical Society, Series B
language:en
Short-container-title:Proc. Amer. Math. Soc. Ser. B

Author:

Patrias Rebecca,Pechenik Oliver

Abstract

Webs are certain planar diagrams embedded in disks. They index and describe bases of tensor products of representations of s l 2 \mathfrak {sl}_2 and s l 3 \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.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology,Discrete Mathematics and Combinatorics,Analysis,Algebra and Number Theory

Link

https://www.ams.org/bproc/2023-10-30/S2330-1511-2023-00191-9/S2330-1511-2023-00191-9.pdf

Reference27 articles.

1. The combinatorics of 𝐀₂-webs;Benkart, Georgia;Electron. J. Combin.,2014

2. Proofs and generalizations of a homomesy conjecture of Propp and Roby;Bloom, Jonathan;Discrete Math.,2016

3. Webs and quantum skew Howe duality;Cautis, Sabin;Math. Ann.,2014

4. Balanced tableaux;Edelman, Paul;Adv. in Math.,1987

5. From dimers to webs;Fraser, Chris;Trans. Amer. Math. Soc.,2019

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Order polynomial product formulas and poset dynamics;Proceedings of Symposia in Pure Mathematics;2024