An explicit bijection between semistandard tableaux and non-elliptic sl_3 webs
Combinatorics
2014-05-14 v1 Geometric Topology
Quantum Algebra
Abstract
The sl_3 spider is a diagrammatic category used to study the representation theory of the quantum group U_q(sl_3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm. Recently, Tymoczko gave a simple version of this bijection in the case that the tableaux are standard and used it to study rotation and joins of webs. We build on Tymoczko's bijection to give a simple and explicit algorithm for constructing all non-elliptic sl_3 webs.
Keywords
Cite
@article{arxiv.1204.1037,
title = {An explicit bijection between semistandard tableaux and non-elliptic sl_3 webs},
author = {Heather M. Russell},
journal= {arXiv preprint arXiv:1204.1037},
year = {2014}
}