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The characteristic quasi-polynomials of the arrangements of root systems

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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
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

Submitter: 数学紀要登録作業用

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