Skew Young Tableaux for KL polynomials of matroids

Abstract: Kazhdan-Lusztig polynomials of matroids were first introduced in 2016 in analogy with the classical ones for the Bruhat order in Coxeter groups. In 2020 it was proved that their coefficients are always non-negative, by interpreting them as the Hilbert series of the local intersection cohomology of some modules associated to the matroid; however, since these polynomials can be completely characterized only using the lattice of flats, a combinatorialist wonders if any result about them can be reobtained exploiting no algebraic geometry results. After introducing the operation of stressed hyperplane relaxation, we show that we can compute these coefficients by counting fillings of special skew tableaux shapes. We will also show how these results can be interpreted using representation theory on the group of automorphisms of the matroid. This is joint work with Luis Ferroni and George Nasr, and Trevor Karn, George Nasr and Nicholas Proudfoot.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

( video )

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Copenhagen-Jerusalem Combinatorics Seminar

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