Factorization of Kazhdan-Lusztig elements for Grassmanians

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.

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