Geodesic
Extended linial hyperplane arrangements for root systems and a conjecture of Postnikov and Stanley
Journal of Algebraic Combinatorics, Tome 10 (1999) no. 3, pp. 207-225.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A hyperplane arrangement is said to satisfy the $ldquo$Riemann hypothesis $rdquo$ 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 [1, 2, 11] 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.
Keywords: hyperplane arrangement, characteristic polynomial, root system 
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     author = {Athanasiadis, Christos A.},
     title = {Extended linial hyperplane arrangements for root systems and a conjecture of {Postnikov} and {Stanley}},
     journal = {Journal of Algebraic Combinatorics},
     pages = {207--225},
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Athanasiadis, Christos A. Extended linial hyperplane arrangements for root systems and a conjecture of Postnikov and Stanley. Journal of Algebraic Combinatorics, Tome 10 (1999) no. 3, pp. 207-225. http://geodesic.mathdoc.fr/item/JAC_1999__10_3_a3/