Intersection cohomology of the symmetric reciprocal plane

2015/04/28 by Proudfoot, Nicholas, Wakefield, Max, Young, Benjamin
#05B35 #20C30 #55N33 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.07348

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].

Related

• Intersection cohomology without spaces
• Singular Hodge theory for combinatorial geometries
• The Kazhdan-Lusztig polynomial of a matroid
• Configuration spaces, \operatornameFS^op-modules, and Kazhdan-Lusztig polynomials of braid matroids
• Intersection Cohomology of reductive varieties