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Abstract
Let w 0 denote the permutation [ n, n−1,…,2,1]. We give a new explicit formula for the Kazhdan–Lusztig polynomials P w 0 w, w 0 x in S n when x indexes an irreducible component of the singular locus of the Schubert variety X w . To do this, we utilize a standard identity that relates P x, w and P w 0 w, w 0 x .
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