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

Abstract

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

arXiv comment8 pages, lots of figures, comments are welcome