The Volume Polynomial of Regular Semisimple Hessenberg Varieties and the Gelfand—Zetlin Polytope

Regular semisimple Hessenberg varieties are subvarieties of the flag variety Flag(ℂn) arising naturally at the intersection of geometry, representation theory, and combinatorics. Recent results of Abe, Horiguchi, Masuda, Murai, and Sato as well as of Abe, DeDieu, Galetto, and Harada relate the volume polynomials of regular semisimple Hessenberg varieties to the volume polynomial of the Gelfand–Zetlin polytope GZ(λ) for λ = (λ1, λ2, …, λn). In …