Modular elements in the lattice L(A) when A is a real reflection arrangement
نویسندگان
چکیده
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 ^ ^ that if W is neither A, nor B,, then the only modular elements are 0, 1 and the atoms of Lw. (~ 1998 Elsevier Science B.V. All rights reserved
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 193 شماره
صفحات -
تاریخ انتشار 1998