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Hokkaido University Preprint Series in Mathematics >
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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