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. 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 sl3 webs.
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The definitive version is available at: http://link.springer.com/article/10.1007/s10801-013-0428-y
Russell, Heather M. "An Explicit Bijection Between Semistandard Tableaux and Non-Elliptic Sl3 Webs." Journal of Algebraic Combinatorics 38, no. 4 (2013): 851-62. doi:10.1007/s10801-013-0428-y.
Russell, Heather M., "An Explicit Bijection Between Semistandard Tableaux and Non-Elliptic sl3 Webs" (2013). Math and Computer Science Faculty Publications. 127.