Two formulae for inverse Kazhdan-Lusztig polynomials in S_n

Details Two formulae for inverse Kazhdan-Lusztig polynomials in S_n Two formulae for inverse Kazhdan-Lusztig polynomials in S_n

2002-06-17

arxiv.org/abs/math/0206164v1

Mathematics

Combinatorics

9 pages, 4 figures

Scientific paper

Let w_0 denote the permutation [n,n-1,...,2,1]. We give two new explicit
formulae for the Kazhdan-Lusztig polynomials P_{w_0w,w_0x} in S_n when x is a
maximal element in 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_0w,w_0x}.

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