Geodesic
Hanlon and Stanley's conjecture and the Milnor fibre of a braid arrangement
Journal of Algebraic Combinatorics, Tome 11 (2000) no. 3, pp. 227-240.

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

Summary: Let $A$ be a real arrangement of hyperplanes. Let $B = B(q)$ be Varchenko's quantum bilinear form of $A$, introduced [15], specialized so that all hyperplanes have weight q. $B(q)$ is nonsingular for all complex q except certain roots of unity. Here, we examine the kernel of B at roots of unity in relation to the topology of the hyperplane singularity. We use Varchenko's work [16] to relate $B(q)$ to a Salvetti complex for the Milnor fibration of $A$. This paper's main result is specific to the arrangement of reflecting hyperplanes associated with the $A _{n - 1}$ root system. We use a geometric property of the Milnor fibre to resolve a conjecture due to Hanlon and Stanley regarding the $\mathfrak S _{ n}$ mathfrakS_n -module structure of the kernel of $B(q)$ at certain roots of unity.
Keywords: hyperplane arrangement, Milnor fibre, quantum bilinear form, braid arrangement 
@article{JAC_2000__11_3_a2,
     author = {Denham, G.},
     title = {Hanlon and {Stanley's} conjecture and the {Milnor} fibre of a braid arrangement},
     journal = {Journal of Algebraic Combinatorics},
     pages = {227--240},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2000__11_3_a2/}
}
TY  - JOUR
AU  - Denham, G.
TI  - Hanlon and Stanley's conjecture and the Milnor fibre of a braid arrangement
JO  - Journal of Algebraic Combinatorics
PY  - 2000
SP  - 227
EP  - 240
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2000__11_3_a2/
LA  - en
ID  - JAC_2000__11_3_a2
ER  - 
%0 Journal Article
%A Denham, G.
%T Hanlon and Stanley's conjecture and the Milnor fibre of a braid arrangement
%J Journal of Algebraic Combinatorics
%D 2000
%P 227-240
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2000__11_3_a2/
%G en
%F JAC_2000__11_3_a2
Denham, G. Hanlon and Stanley's conjecture and the Milnor fibre of a braid arrangement. Journal of Algebraic Combinatorics, Tome 11 (2000) no. 3, pp. 227-240. http://geodesic.mathdoc.fr/item/JAC_2000__11_3_a2/