Physical Sciences and Mathematics Commons^™

A Simple Bijection Between Standard 3×N Tableaux And Irreducible Webs For 𝔰𝔩3, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

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 on representations correspond to graph-theoretic operations on webs. Kuperberg developed spiders for rank 2 Lie algebras and 𝔰𝔩₂. Building on a result of Kuperberg’s, Khovanov-Kuperberg found a recursive algorithm giving a bijection between standard Young tableaux of shape 3 × n and irreducible webs for 𝔰𝔩₃whose boundary vertices are all sources. In this paper, we give a simple and explicit map from standard Young tableaux of shape 3 …