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Full-Text Articles in Physical Sciences and Mathematics
A Simple Bijection Between Standard 3×N Tableaux And Irreducible Webs For 𝔰𝔩3, Julianna Tymoczko
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 …