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

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 $h$.

(Appendix by Sara Billey and Jonathan Weed)