Corpus ID: 237485509

# Tableau evacuation and webs

```@inproceedings{Patrias2021TableauEA,
title={Tableau evacuation and webs},
author={Rebecca Patrias and Oliver Pechenik},
year={2021}
}```
• Published 10 September 2021
• Mathematics
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.

#### References

SHOWING 1-10 OF 21 REFERENCES
Promotion and cyclic sieving via webs
• Mathematics
• 2008
We show that Schützenberger’s promotion on two and three row rectangular Young tableaux can be realized as cyclic rotation of certain planar graphs introduced by Kuperberg. Moreover, following workExpand
A Simple Bijection Between Standard 3 ×n Tableaux and Irreducible Webs for ? ? 3
Combinatorial spiders are a model for the invariant space of the tensor product of representations. The basic objects, webs, are certain directed planar graphs with boundary; algebraic operations onExpand
An explicit bijection between semistandard tableaux and non-elliptic sl3 webs
The sl3 spider is a diagrammatic category used to study the representation theory of the quantum group Uq(sl3). The morphisms in this category are generated by a basis of non-elliptic webs.Expand
The transition matrix between the Specht and web bases is unipotent with additional vanishing entries
• Mathematics
• 2017
We compare two important bases of an irreducible representation of the symmetric group: the web basis and the Specht basis. The web basis has its roots in the Temperley-Lieb algebra andExpand
THE POLYTABLOID BASIS EXPANDS POSITIVELY INTO THE WEB BASIS
• Mathematics
• Forum of Mathematics, Sigma
• 2019
We show that the transition matrix from the polytabloid basis to the web basis of the irreducible \$\mathfrak{S}_{2n}\$ -representation of shape \$(n,n)\$ has nonnegative integer entries. This proves aExpand
The Combinatorics of A 2-webs
• 2014
The nonelliptic A2-webs with k “+”s on the top boundary and 3n − 2k “−”s on the bottom boundary combinatorially model the space Homsl3(V,V) of sl3-module maps on tensor powers of the naturalExpand
Promotion on generalized oscillating tableaux and web rotation
It is shown that this promotion corresponds to rotation of the irreducible \$A_2\$-webs of G. Kuperberg. Expand
Young Tableaux: With Applications to Representation Theory and Geometry
Part I. Calculus Of Tableux: 1. Bumping and sliding 2. Words: the plactic monoid 3. Increasing sequences: proofs of the claims 4. The Robinson-Schensted-Knuth Correspondence 5. TheExpand
Balanced Tableaux
In this paper we define and study a new class of combinatorial objects called balanced tableaux. They are obtained by labeling the Ferrets diagram of an integer partition, so that certain rankExpand
Canonical bases and self-evacuating tableaux
Let g be a complex semisimple Lie algebra. In this paper, we prove that the action of a certain involution on canonical bases for irreducible g-modules deened by Lusztig agrees with the action of aExpand