Factorization of Kazhdan–Lusztig Elements for Grassmanians

Abstract

We show that the Kazhdan–Lusztig basis elements $C_w$ of the Hecke algebra of the symmetric group, when $w \in S_n$ corresponds to a Schubert subvariety of a Grassmann variety, can be written as a product of factors of the form $T_i + f_j(v)$, where $f_j$ are rational functions.