Transitioning between tableaux and spider bases for Specht modules

Abstract: 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.