Bases of the intersection cohomology of Grassmannian Schubert varieties

The parabolic Kazhdan–Lusztig polynomials for Grassmannians can be computed by counting Dyck partitions. We “lift” this combinatorial formula to the corresponding category of singular Soergel bimodules obtain bases Hom spaces between indecomposable objects. In particular, we describe intersection cohomology Schubert varieties in parametrized partitions which extend (after dualizing) classical basis ordinary cohomology.