Research on representations and categories of association schemes

• Project/Area Number: 21540011
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Shinshu University
• Principal Investigator: HANAKI Akihide 信州大学, 理学部, 教授 (50262647)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: アソシエーション / スキーム / 表現 / 圏 / アソシエーション・スキーム / クリフォード理論 / アソシエーションスキーム / 指標 / 代数的組合せ論

Research Abstract

A category of association schemes was defined and some notions were understood categorically. Clifford theory of association schemes and their strongly normal closed subsets was proved. Also a dual, induction and restriction are exchanged, of Clifford theory of association schemes and their algebraic fusions was proved. Some Terwilliger algebras and integral standard generalized table algebras were obtained.

Research Products

• [Journal Article] Commutativity of association schemes of order pq (2013)
  • Author(s): A. Hanaki, M. Hirasaka
  • Journal Title: East Asian Math. J Volume: 29 (1) Issue: 1 Pages: 39-52
  • DOI: 10.7858/eamj.2013.004
  • Peer Reviewed
• [Journal Article] A construction of integral standard generalized table algebras from parameters of projective geometries (2013)
  • Author(s): Y. Asaba, A. Hanaki
  • Journal Title: Israel J. Math Volume: 194 (1) Issue: 1 Pages: 395-408
  • DOI: 10.1007/s11856-012-0083-3
  • NAID: 120007114338
  • Peer Reviewed
• [Journal Article] Clifford type theorems for association schemes and their algebraic fusions (2012)
  • Author(s): A. Hanaki
  • Journal Title: J. Algebra. Volume: 363 Pages: 1-7
  • DOI: 10.1016/j.jalgebra.2012.04.021
  • NAID: 120007114250
  • Peer Reviewed
• [Journal Article] A. Hanaki, K. Kim, Y. Maekawa (2011)
  • Author(s): Terwilliger algebras of direct and wreath products of association schemes
  • Journal Title: J. Algebra. Volume: 343 (1) Issue: 1 Pages: 195-200
  • DOI: 10.1016/j.jalgebra.2011.05.035
  • Peer Reviewed
• [Journal Article] aithful representations of association schemes (2011)
  • Author(s): A. Hanaki
  • Journal Title: Proc. Amer. Math. Soc Volume: 139 (9) Issue: 9 Pages: 3191-3193
  • DOI: 10.1090/s0002-9939-2011-11026-8
  • Peer Reviewed
• [Journal Article] A category of association schemes (2010)
  • Author(s): A. Hanaki
  • Journal Title: J. Combin. Theory Ser. A Volume: 117 Issue: 8 Pages: 1207-1217
  • DOI: 10.1016/j.jcta.2009.10.004
  • NAID: 120007114252
  • Peer Reviewed
• [Journal Article] A category of association schemes (2010)
  • Author(s): Akihide Hanaki
  • Journal Title: Journal of Combinatorial Theory, Series A Volume: 117 Pages: 1207-1217
  • NAID: 120007114252
  • Peer Reviewed
• [Journal Article] Representations of finite association schemes (2009)
  • Author(s): A. Hanaki
  • Journal Title: European J. Combin. Volume: 30 Issue: 6 Pages: 1477-1496
  • DOI: 10.1016/j.ejc.2008.11.004
  • NAID: 120007114253
  • Peer Reviewed
• [Journal Article] Clifford theory for association schemes (2009)
  • Author(s): A. Hanaki
  • Journal Title: J. Algebra. Volume: 321 (6) Issue: 6 Pages: 1686-1695
  • DOI: 10.1016/j.jalgebra.2009.01.006
  • Peer Reviewed
• [Journal Article] A modular absolute bound condition for primitive association schemes (2009)
  • Author(s): A. Hanaki, I. Ponomarenko
  • Journal Title: J. Algebraic Combin Volume: 29 Issue: 4 Pages: 447-456
  • DOI: 10.1007/s10801-008-0145-0
  • NAID: 120007114343
  • Peer Reviewed
• [Journal Article] Chifford theory for association schemes (2009)
  • Author(s): Akihide Hanaki
  • Journal Title: Journal of Algebra 321 Pages: 1686-1695
  • Peer Reviewed
• [Journal Article] Representations of finite association schemes (2009)
  • Author(s): Akihide Hanaki
  • Journal Title: European Journal of Combinatorics 30 Pages: 1477-1496
  • NAID: 120007114253
  • Peer Reviewed
• [Journal Article] A construction of integral standard generalized table algebras from parameters of projective geometries
  • Author(s): Y.Asaba, A.Hanaki
  • Journal Title: Israel J.Math. Volume: (掲載決定)
  • NAID: 120007114338
  • Peer Reviewed
• [Presentation] アソシエーションスキームの表現入門 (2013)
  • Author(s): 花木章秀
  • Organizer: 第5回若手会セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2013-03-16
• [Presentation] Quasi-permutation characters of special p-groups (2012)
  • Author(s): 花木章秀
  • Organizer: 第24回有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス
  • Year and Date: 2012-07-28
• [Presentation] Quasi-permutation characters of special p-groups (2012)
  • Author(s): 花木章秀
  • Organizer: 第 24 回有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス
• [Presentation] Clifford theory for algebraic fusions of association schemes (2011)
  • Author(s): 花木章秀
  • Organizer: 第23回有限群論草津セミナー
  • Place of Presentation: 草津セミナーハウス
  • Year and Date: 2011-07-30
• [Presentation] Clifford theory for algebraic fusions of association schemes (2011)
  • Author(s): 花木章秀
  • Organizer: 有限群草津セミナー
  • Place of Presentation: 草津セミナーハウス
  • Year and Date: 2011-07-30
• [Presentation] Clifford Theory for Association Schemes (2011)
  • Author(s): 花木章秀
  • Organizer: 信州代数セミナー
  • Place of Presentation: 信州大学
  • Year and Date: 2011-07-11
• [Presentation] Categories of association schemes and coherent configurations (2009)
  • Author(s): 花木章秀
  • Organizer: 第26回代数的組合せ論シンポジウム
  • Place of Presentation: 山形「遊学館」
  • Year and Date: 2009-06-26
• [Presentation] Categories of association schemes and coherent configurations (2009)
  • Author(s): 花木章秀
  • Organizer: 第26回代数的組合せ論シンポジウム
  • Place of Presentation: 遊学館(山形)
  • Year and Date: 2009-06-26
• [Remarks] 計算機による小さなアソシエーション・スキームの分類結果とその指標表
  • URL: http://math.sinshu-u.ac.jp/~hanaki/
• [Remarks]
  • URL: http://math.shinshu-u.ac.jp/~hanaki/
• [Remarks]
  • URL: http://kissme.shinshu-u.ac.jp/as/