A formula for certain inverse Kazhdan-Lusztig polynomials in Sn

Let w0 denote the permutation [n, n - 1, ..., 2, 1]. We give a new explicit formula for the Kazhdan-Lusztig polynomials Pw0w,w0x in Sn when x indexes an irreducible component of the singular locus of the Schubert variety Xw. To do this, we utilize a standard identity that relates Px,w and Pw0w,w0x.

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