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Title:

A geometric interpretation of the characteristic polynomial of reflection arrangements

Document type:
Zeitschriftenaufsatz
Author(s):
Drton, Mathias; Klivans, Caroline J.
Abstract:
We consider projections of points onto fundamental chambers of finite real reflection groups. Our main result shows that for groups of types An,Bn, and Dn, the coefficients of the characteristic polynomial of the reflection arrangement are proportional to the spherical volumes of the sets of points that are projected onto faces of a given dimension. We also provide strong evidence that the same connection holds for the exceptional, and thus all, reflection groups. These results naturally extend...     »
Keywords:
Characteristic polynomial, Coxeter group, hyperplane arrangement, order-restricted statistical inference, reflection group
Dewey Decimal Classification:
510 Mathematik
Journal title:
Proceedings of the American Mathematical Society
Year:
2010
Journal volume:
138
Year / month:
2010-04
Quarter:
2. Quartal
Month:
Apr
Journal issue:
08
Pages contribution:
2873-2887
Language:
en
Fulltext / DOI:
doi:10.1090/s0002-9939-10-10369-4
Publisher:
American Mathematical Society (AMS)
Print-ISSN:
0002-9939
E-ISSN:
1088-6826
Notes:
Published electronically: April 8, 2010
Status:
Verlagsversion / published
Date of publication:
08.04.2010
Format:
Text
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