کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4587004 | 1334125 | 2009 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Reflection groups acting on their hyperplanes
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
After having established elementary results on the relationship between a finite complex (pseudo-)reflection group W⊂GL(V) and its reflection arrangement A, we prove that the action of W on A is canonically related with other natural representations of W, through a ‘periodic’ family of representations of its braid group. We also prove that, when W is irreducible, then the squares of defining linear forms for A span the quadratic forms on V, which imply |A|⩾n(n+1)/2 for n=dimV, and relate the W-equivariance of the corresponding map with the period of our family.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 322, Issue 8, 15 October 2009, Pages 2848-2860
Journal: Journal of Algebra - Volume 322, Issue 8, 15 October 2009, Pages 2848-2860