  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 to obtain bases of the Hom
spaces between indecomposable objects. In particular, we describe bases of
intersection cohomology of Schubert varieties in Grassmannians parametrized by
Dyck partitions which extend (after dualizing) the classical Schubert basis of
the ordinary cohomology.

Representation Theory