Modular elements in the lattice L(A) when A is a real reflection arrangement

✍ Scribed by H. Barcelo; E. Ihrig

• Book ID: 104114150
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 362 KB
• Volume: 193
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(98)00134-4

✦ Synopsis

Let W be a real reflection group, and let Lw denote the lattice consisting of all possible intersections of reflecting hyperplanes of reflections in W. Let pw(t) be the characteristic polynomial of Lw. To every element X of Lw there corresponds a parabolic subgroup of W denoted by Gal(X). If W is irreducible, we show that an element X of Lw is modular if and only if pG,~(x)(t) divides pw(t). This characterization is not true if W is not irreducible. Also, we show ^ ^