  Using combinatorial properties of symmetric polynomials, we compute
explicitly the Soergel modules for some permutations whose corresponding
Schubert varieties are rationally smooth. We build from them diagram algebras
whose module categories are equivalent to the subquotient categories of the BGG
category $\mathcal{O}(\mathfrak{gl}_n)$ which show up in categorification of
$\mathfrak{gl}(1|1)$-representations. We construct diagrammatically the graded
cellular structure and the properly stratified structure of these algebras.
