Geodesic
On a family of hyperplane arrangements related to the affine Weyl groups
Journal of Algebraic Combinatorics, Tome 6 (1997) no. 4, pp. 331-338.

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

Summary: Let $k$ Ĩ $Z$ k $\in Z$ , let $H( a, k) H(\alpha ,k)$ be the hyperplane ${ v$ Ĩ $V$: á a, $v \~n = k}$ { v $\in V$:left$\langle {\alpha ,v}$ right$\rangle = k$} . We define a set of hyperplanes $H = $ H( d,1): d Ĩ F ^+ $ \`E$ H( d,0): d Ĩ F ^+ mathcalH = $ H(delta,1):deltainPhi^ + } cup{ H(delta,0):deltainPhi$^ + \} . This hyperplane arrangement is significant inthe study of the affine Weyl groups. In this paper it is shown that thePoincar\'e polynomial of $H$ \mathcal{H} is $( 1 + ht ) ^ n left( 1 + ht right)$^n , where $n$ is the rank of $PHgr$ and $h$ is the Coxeter number of the finiteCoxeter group corresponding to $PHgr$.$
Keywords: hyperplane arrangement, Weyl group, Poincaré polynomial 
@article{JAC_1997__6_4_a2,
     author = {Headley, Patrick},
     title = {On a family of hyperplane arrangements related to the affine {Weyl} groups},
     journal = {Journal of Algebraic Combinatorics},
     pages = {331--338},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1997__6_4_a2/}
}
TY  - JOUR
AU  - Headley, Patrick
TI  - On a family of hyperplane arrangements related to the affine Weyl groups
JO  - Journal of Algebraic Combinatorics
PY  - 1997
SP  - 331
EP  - 338
VL  - 6
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_1997__6_4_a2/
LA  - en
ID  - JAC_1997__6_4_a2
ER  - 
%0 Journal Article
%A Headley, Patrick
%T On a family of hyperplane arrangements related to the affine Weyl groups
%J Journal of Algebraic Combinatorics
%D 1997
%P 331-338
%V 6
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_1997__6_4_a2/
%G en
%F JAC_1997__6_4_a2
Headley, Patrick. On a family of hyperplane arrangements related to the affine Weyl groups. Journal of Algebraic Combinatorics, Tome 6 (1997) no. 4, pp. 331-338. http://geodesic.mathdoc.fr/item/JAC_1997__6_4_a2/