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The characteristic quasi-polynomials of the arrangements of root systems
Title: | The characteristic quasi-polynomials of the arrangements of root systems |
Authors: | Kamiya, Hidehiko Browse this author | Takemura, Akimichi Browse this author | Terao, Hiroaki Browse this author |
Issue Date: | Jul-2007 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 865 |
Start Page: | 1 |
End Page: | 24 |
Abstract: | For an irreducible root system R, consider a coefficient matrix S of the positive roots with respect to the associated simple roots. Then S defines an arrangement of “hyperplanes” modulo a positive integer q. The cardinality of the complement of this arrangement is a quasi-polynomial of q, which we call the characteristic quasi-polynomial of R. This paper gives the complete list of the characteristic quasi-polynomials of all irreducible root systems, and shows that the characteristic quasi-polynomial of an irreducible root system R is positive at q 2 Z>0 if and only if q is greater than or equal to the Coxeter number of R. Key words: characteristic quasi-polynomial, elementary divisor, hyperplane arrangement, root system. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69674 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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