超平面配置の諸相

2011 Fiscal Year Annual Research Report

• Project/Area Number: 21340001
• Research Institution: Hokkaido University
• Principal Investigator: 寺尾 宏明 北海道大学, 大学院・理学研究院, 教授 (90119058)
• Keywords: 代数的組合せ論 / 超平面配置

Research Abstract

23年度は,昨年度開始した(A)重複度をもつCoxeter配置に関する研究を行った.また(B)整数上で定義される超平面配置をmを法とした周期性に関する研究も進めた.研究成果としては,(A)については,阿部拓郎(京大・工)・Gao Ruimei(東北師範大学),Donghe Pei(東北師範大学)を共同研究者として[A1]と[A2]の論文を出版した.特に[A2]は,昨年度のSuyama-TeraoのA型の結果をD型について得たもので,ここでもベルヌーイ多項式が登場したことは特筆に値する.[A3]は現在投稿中である.
(A)の意義:複数のワイル群のShi配置に関してベルヌーイ多項式との関連が明らかになった.
(B)の意義:研究が進んでいなかった整数上の配置について周期性を初めて見出した[B].
[A1] The freeness of Shi-Catalan arrangements. (with T.Abe) European J.Combin.32 (2011), 1191-1198
[A2] The Shi arrangement of the type D.(with R.Gao, D.Pei) Proc.Japan Acad.Ser.A Math.Sci., 88 (2012), 41-45
[A3] Simple-root bases for Shi arrangements. (arXiv:1111.3510) (with T.Abe) preprint
[B] Periodicity of non-central integral arrangements modulo positive integers. (with H.Kamiya, A.Takemura) Ann.Combin., 15 (2011), 449-464

Research Products

• [Journal Article] The Shi arrangements and the Bernoulli polynomials (2012)
  • Author(s): Daisuke Suyama, Hiroaki Terao
  • Journal Title: Bull.London Math.Soc. Volume: (未定)(掲載確定)
  • DOI: doi:10.1112/blms/bdr118
  • Peer Reviewed
• [Journal Article] Arrangements stable under the Coxeter groups (2012)
  • Author(s): Hidehiko Kamiya, Akimichi Takemura, Hiroaki
  • Journal Title: Configuration Spaces : Geometry, Topology and Combinatorics, Proceedings of a special period at the De Giorgi Center, Scuola Normale in Pisa, May-June. 2010, Birkhauser Volume: (未定)(掲載確定)
  • Peer Reviewed
• [Journal Article] The Shi arrangement of the type $D_\ell$ (2012)
  • Author(s): Ruimei Gao, Donghe Pei, Hiroaki Terao
  • Journal Title: Proc.Japan Acad.Ser.A Math.Sci. Volume: 88 Pages: 41-45
  • Peer Reviewed
• [Journal Article] The freeness of Shi-Catalan arrangements (2011)
  • Author(s): Takuro Abe, Hiroaki Terao
  • Journal Title: European J.Combin. Volume: 32 Pages: 1191-1198
  • DOI: doi:10.1016/j.ejc.2011.06.005
  • Peer Reviewed
• [Presentation] Simple bases for the logarithmic derivation modules of the generalized Shi arrangements (2011)
  • Author(s): 寺尾宏明
  • Organizer: Topics in the Theory of Weyl Groups and Root Systems (Sekiguchi 60)
  • Place of Presentation: 東京大学(東京都)(招待講演)
  • Year and Date: 2011-09-20
• [Presentation] The Shi arrangements and the Bernoulli numbers (2011)
  • Author(s): 寺尾宏明
  • Organizer: the Special Session on "The Algebraic Geometry and Topology of Hyperplane Arrangements" at an AMS Sectional Meeting
  • Place of Presentation: University of Hawaii at Manoa (USA)(招待講演)
  • Year and Date: 2011-04-09
• [Remarks]
  • URL: http://www.math.sci.hokudai.ac.jp/~terao/