EXTENDED LINIAL HYPERPLANE ARRANGEMENTS

FOR ROOT SYSTEMS

AND A CONJECTURE OF POSTNIKOV AND STANLEY

CHRISTOS A. ATHANASIADIS

Abstract. A hyperplane arrangement is said to satisfy the “Riemann hypothesis” if all roots of its characteristic polynomial have the same real part. This property was conjectured by Postnikov and Stanley for certain families of arrangements which are defined for any irreducible root system and was proved for the root system A_{n−1}. The proof is based on an explicit formula for the characteristic polynomial, which is of independent combinatorial significance. Here our previous derivation of this formula is simplified and extended to similar formulae for all but the exceptional root systems. The conjecture follows in these cases.