Mask Formulas for Cograssmannian Kazhdan-Lusztig Polynomials

We give two constructions of sets of masks on cograssmannian permutations that can be used in Deodhar’s formula for Kazhdan–Lusztig basis elements of the Iwahori–Hecke algebra. The constructions are respectively based on a formula of Lascoux–Schützenberger and its geometric interpretation by Zelevinsky. The first construction relies on a basis of the Hecke algebra constructed from principal lower order ideals in Bruhat order and a translation of this basis into sets of masks. The second construction relies on an interpretation of masks as cells of the Bott–Samelson resolution. These constructions give distinct answers to a question of Deodhar.