The research of algebra as fundamental tools of Mathematical Science

• Project/Area Number: 07304004
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 総合
• Research Field: Algebra
• Research Institution: KYUSHU UNIVERSITY
• Principal Investigator: KOIKE Masao Graduate School of Math.KYUSHU UNIVERSITY Professor, 大学院・数理学研究科, 教授 (20022733)
• Co-Investigator(Kenkyū-buntansha): KATARA Toshiyuki Tokyo Univ., Graduate School of Mathematics.Prof., 大学院・数理科学研究科, 教授 (40108444) ; KITAOKA Yoshiyuki Nagoya Univ., Poly Matheratics, Prof., 大学院・多元数理科学研究科, 教授 (40022686) ; TANISAKI Toshiyuki Hiroshima Univ.Mathematics, Prof., 理学部, 教授 (70142916) ; MORITA Yasuo Mathematical Institude of Tohoku Univ., prof., 大学院・理学研究科, 教授 (20011653) ; BANNAI Eiichi Graduate School of Math.KYUSHU UNIVERSITY Professor, 大学院・数理学研究科, 教授 (10011652) ; 白谷 克巳 九州大学, 大学院数理学研究科, 教授 (80037168)
• Project Period (FY): 1995 – 1996
• Project Status: Completed (Fiscal Year 1996)
• Budget Amount: ¥20,100,000 (Direct Cost: ¥20,100,000); Fiscal Year 1996: ¥9,000,000 (Direct Cost: ¥9,000,000); Fiscal Year 1995: ¥11,100,000 (Direct Cost: ¥11,100,000)
• Keywords: Algebra / Algebraic Number Theory / Algebraic Combinatorics / Commutative ring theory / Modular forms / Representation Theory / Aralytic Number Theory / 代数的組み合せ論 / 可換環論 / 可挽環論 / 代数群

Research Abstract

We held 21 symposiums on many topics in algebra. Among them, there are (1) The 40th, 41st Algebra Symposiums, (2) The 12th Symposium on algebraic combinatorics, (3) The 3rd, 4th Summer School on modular forms, (4) The 28th Symposium on ring theory,
(5) Conference on semi group, language and related topics, (6) The 17th Symposium on commutative ring theory, (7) International conference on analytic number theory, (8) The 29th Symposium on ring theory and representation theory, (9) The 6th Symposium on representation theory of algebra, (10) Conference on algebraic number theory and Fermat's Last Theorem, (11) Conference on computation and algebrs, (12) Conference on mondular forms on algebraic groups, (13) Conference on zeta functions and modular forms, (14) conference on number theory, (15) Workshop on Thompson series.
The details of topics which are announced and discussed in these symposiums are published as proceedings.

Research Products

• [Publications] M.Koike: "A note on hypergeometric polynomials over the finite fields" Proc.Jangjun Intern.Conf.of Math.Sciences. to appear. (1997)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] E.Bannai: "Generaliged generaliged spin models (four-weight spin models)" Pacific J.Math.170. 1-16 (1995)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Tanisaki: "Kazhdan-Lusztig conjecture for affire hie alg.with negatie level II" Duke Math.J.84. 771-813 (1996)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] Y.Morita: "Remarks on a conjecture of Batyrev and Manin" Tokoku Math.J.to appear. (1997)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] Y.Kitaoka: "The minimum and the primitive representation of positive df.quad." forms II.Nagoya Math.J.141. 1-27 (1996)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] T.Katura: "Multi canonical systems of elliptic sinfaces in small char." Compositio Math.97. 119-134 (1995)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] 谷崎俊之: "D加群と代数群" シュプリンガー・フェアラーク東京, 308 (1995)
  • Description: 「研究成果報告書概要(和文)」より
• [Publications] M.Koike: "A note on hypergesmetric polynomials over the finite fields" Proc.Jangiur Intern.Conf.of Meth.Sci.(to appear). (1997)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] E.Bannai and E.Bannai: "Generalized generalized spin models (four-weiglt spin model)" Pacific.J.Math.170. 1-16 (1995)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T.Tamisaki and M.Kashiwara: "Kazhdan-Luszting conjecture for affice his algebra with megative level II" Duke Math.J.84. 779-813 (1996)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] Y.Morita: "Remarks on a conjecture of Batirew and Manin" Tokoku Math.J.(to appear). (1997)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] Y.Kitaoka: "The minimum and the primitive representation of positive defirite quadratic forme II" Nagoya Math.J.141. 1-27 (1996)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] T.Katura: "Multicanonical system of elliptin surfaces in small characteristic" Compositro Math.97. 119-134 (1995)
  • Description: 「研究成果報告書概要(欧文)」より
• [Publications] M.Koike: "A note on hypergeometric polynomials over the finite fields" Proc.Jangjun Intern.Conf.of Math.Sciences. (to appear). (1997)
• [Publications] E.Bannai: "Generaliged generaliged opin models(four-weight spin models)" Pacific J.Math.170. 1-16 (1995)
• [Publications] T.Tanisaki: "Kafhdan-Lusztig conjecture for abbine hie alg.with negative level II" Duke Math.J.84. 771-813 (1996)
• [Publications] Y.Morita: "Remarks on a conjecture of Batyrev and Manin" Tokoku Math.J.(to appear). (1997)
• [Publications] Y.Kitaoka: "The minimum and the primitive representation of positive of.guad." Forns II,Nagoya Math.J.141. 1-27 (1996)
• [Publications] T.Katura: "Multicanonical systems of elliptic swfaces in small char." Compositio Math.97. 119-134 (1995)
• [Publications] M. Koike: "Orthogonal matrices obtained from hujpergesmetric series over finite fields and elliptic curues over finite falds" Hiroshima Math. J.25. 43-52 (1995)
• [Publications] Eiichi Bannai: "Generaliged generaliged Spin models(four weight spin-models)" Pacific J. Math.170. 1-16 (1995)
• [Publications] Eiichi Bannai: "Construction of Jacobi forms from certain combinatorial polynomials" Proc. Japan Acad.72. 24-27 (1996)
• [Publications] T. Tanisaki: "Kazhdan-Lusztig conjecture for affine Lie algebra with negotive weigbt" Duke Mathemctical J.77. 21-62 (1995)
• [Publications] K. Shiratani: "On a rationality problem of Jacobi sums" Acta Arithmetica. (to appear).
• [Publications] Y. Morita: "Models of ruled surfaces over an algebraic number field" Tokoku Math. J.(to appear).
• [Publications] 谷崎 俊之: "D加群と代数群" シュプリンガー・フェアラーク東京, 308 (1995)