2024-03-29T11:54:52Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696742022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116The characteristic quasi-polynomials of the arrangements of root systemsKamiya, HidehikoTakemura, AkimichiTerao, Hiroakiopen access410For 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.Department of Mathematics, Hokkaido University2007-07engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84015http://hdl.handle.net/2115/6967410.14943/84015Hokkaido University Preprint Series in Mathematics865124https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69674/1/pre865.pdfapplication/pdf219.11 KB2007-07