Permutations with Kazhdan-Lusztig polynomial P_{id,w}(q) = 1 + q^h

TL;DR

This paper proves a conjecture characterizing permutations with specific Kazhdan-Lusztig polynomials using geometric resolutions and polynomial calculation methods.

Contribution

It introduces a proof of Billey and Braden's conjecture linking permutation properties to Kazhdan-Lusztig polynomials.

Findings

Characterization of permutations with P_{id,w}(q)=1+q^h

Application of resolutions of singularities in proof

Use of Polo's method for polynomial calculation

Abstract

Using resolutions of singularities introduced by Cortez and a method for calculating Kazhdan-Lusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with Kazhdan-Lusztig polynomial P_{id,w}(q)=1+q^h for some h.