Richmond–Slofstra's Grassmannian BP-decomposition conjecture

Let $W$ be a Coxeter group and let $w\in W$ be rationally smooth. A Grassmannian BP decomposition is a BP decomposition of $w$ with the Grassmannian property described in the paper.

Richmond–Slofstra's conjecture. The element $w$ has a Grassmannian BP decomposition.

In finite type, rationally smooth Schubert varieties can be expressed as iterated bundles of Grassmannian Schubert varieties. The conjecture asks whether this phenomenon extends to arbitrary Coxeter groups and remains open in the stated generality.