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Regarding the Specht modules associated to the two-row partition $(n,n)$, we provide a combinatorial path model to study the transitioning matrix from the tableau basis to the $A_1$-web basis (i.e. cup diagrams), and prove that the entries in this matrix are positive in the upper-triangular portion with respect to a certain partial order. Regarding the Specht modules associated to the three-row partition $(n,n,n)$, we construct an isomorphism using the tableau basis and the $A_2$-web basis (i.e. spiders), and provide a graphical calculus-based algorithm to compute the coefficients of the transitioning matrix.

Transitioning Between Tableaux and Spider Bases for Specht Modules