Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties

摘要

Motivated by a 1993 conjecture of Stanley and Stembridge, Shareshian and Wachs conjectured that the characteristic map takes the character of the dot action of the symmetric group on the cohomology of a regular semisimple Hessenberg variety to omega X-G(t), where X-G(t) is the chromatic quasisymmetric function of the incomparability graph G of the corresponding natural unit interval order, and omega is the usual involution on symmetric functions. We prove the Shareshian-Wachs conjecture.