Characteristic polynomials of Linial arrangements for exceptional root systems

Abstract

The (extended) Linial arrangement LΦm is a certain finite truncation of the affine Weyl arrangement of a root system Φ with a parameter m. Postnikov and Stanley conjectured that all roots of the characteristic polynomial of LΦm have the same real part, and this has been proved for the root systems of classical types.In this paper we prove that the conjecture is true for exceptional root systems when the parameter m is sufficiently large.The proof is based on representations of the characteristic quasi-polynomials in terms of Eulerian polynomials.