In this talk I will introduce the weak Bruhat order W_n on S_n and the strong Sperner property of Posets and show that W_n is strongly Sperner with approaches from two different works. Stanley conjectured an order rising operator U on \mathbb{C}W_n and showed that if U^{r-2k} is invertible then W_n is strongly Sperner. In the first work, Gaetz and Gao constructed an order lowering operator D which led to an sl_2 representation of \mathbb{C}W_n and used representation theory of sl_2 to prove invertibility. In the second work, Speyer et al. proved a determinantal formula of U^{r-2k} conjectured by Stanley, through showing that the divergence operator acts on Schubert Polynomials as the operator U and this implies invertibility of U^{r-2k}.