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Motivated by the M-diagrams defined by Tymoczko, we show that these locallynon-crossing $\mathfrak{sl}_3$-webs form a basis of the Specht module for thepartition $(n,n,n)$. They further admit a unitriangular base change to both thepolytabloid basis and the non-elliptic web basis.

M-diagram basis of the Specht module for $(n,n,n)$