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

2023/05/08 by Jieru Zhu, Zhu, Jieru
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2305.04731

Abstract

Motivated by the M-diagrams defined by Tymoczko, we show that these locally non-crossing \mathfraksl₃-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.

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