An explicit bijection between semistandard tableaux and non-elliptic sl_3 webs

摘要

The sl_3 spider is a diagrammatic category used to study the representationtheory of the quantum group U_q(sl_3). The morphisms in this category aregenerated by a basis of non-elliptic webs. Khovanov- Kuperberg observed thatnon-elliptic webs are indexed by semistandard Young tableaux. They establishthis bijection via a recursive growth algorithm. Recently, Tymoczko gave asimple version of this bijection in the case that the tableaux are standard andused it to study rotation and joins of webs. We build on Tymoczko's bijectionto give a simple and explicit algorithm for constructing all non-elliptic sl_3webs.