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arXiv · 1504.07348

Intersection cohomology of the symmetric reciprocal plane

Nicholas Proudfoot·Max Wakefield·Benjamin Young
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Abstract

We compute the Kazhdan-Lusztig polynomial of the uniform matroid of rank n-1 on n elements by proving that the i-th coefficient of is equal to the number of ways to choose i non-intersecting chords in an (n-i+1)-gon. We also show that the corresponding intersection cohomology group is isomorphic to the irreducible representation of the symmetric group associated to the partition [n-2i,2,...,2].

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Nicholas Proudfoot, Max Wakefield, Benjamin Young. 2015-12-20. Intersection cohomology of the symmetric reciprocal plane. https://arxiv.org/abs/1504.07348

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