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1999 Fiscal Year Final Research Report Summary

Finite Groups (Sporadic Simple Groups) and Related Topics

Research Project

Project/Area Number 09440006
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionChiba University

Principal Investigator

KITAZUME Masaaki  Faculty of Science, Chiba University Associate Professor, 理学部, 助教授 (60204898)

Co-Investigator(Kenkyū-buntansha) SUGIYAMA Ken-ichi  Faculty of Science, Chiba University Associate Professor, 理学部, 助教授 (90206441)
NOZAWA Sohei  Faculty of Science, Chiba University Professor, 理学部, 教授 (20092083)
KOSHITANI Shigeo  Faculty of Science, Chiba University Professor, 理学部, 教授 (30125926)
MUNEMASA Akihiro  Kyushu University, Associate Professor, 数理学研究科, 助教授 (50219862)
MIYAMOTO Masahiko  University of Tsukuba, Professor, 数学系, 教授 (30125356)
Project Period (FY) 1997 – 1999
KeywordsFinite Groups / Simple Groups / Designs / Codes / Lattices / Graphs / Vertex Operator Algebras / Monster simple group
Research Abstract

We have studied finite simple groups and related graphs, designs, codes, lattices and vertex operator algebras. Main results are as follows :
1. The 2- and 3-radical subgroups of Fischer's simple groups FィイD222ィエD2, FィイD223ィエD2, F'ィイD224ィエD2 have been classified.
2. Two kinds of non-split extensions of OィイD27ィエD2(3) have been constructed explicitly by using Dickson's trilinear form and some special Moufang loop.
3. By using a lattice VOA, a new proof of the Borwein identity has been given.
4. New VOAs related to ternary codes have been introduced, and the irreducible representations of L(ィイD74(/)5ィエD7, 0) 【symmetry】 L(ィイD74(/)5ィエD7, 3) have been determined.
5. By using an embedding ィイD82ィエD8AィイD312(/)2ィエD3 into the Leech lattice and a ZィイD22ィエD2 × ZィイD22ィエD2-code, some decomposition of the Moonshine VOA has been given.
6. Some 5-designs invariant by PSL(2, 23) and related to S(5, 8, 24) have been classified.
7. A simple characterization of S(5, 8, 24) (or Golay code) has been given.
8. The Niemeier lattices have been constructed form ZィイD24ィエD2-codes, and their embeddings of them into 1/ィイD82ィエD8 times the Leech lattice have been given.
9. The exceptional graphs embedded into the root system EィイD28ィエD2 have been classified.
10. Even unimodular Gaussian (resp. Quaternionic) lattices of dimension 12 (resp. 6) have been classified.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] M.Kitazume,A.Munemasa: "New 5-Designs with Automorphism Group PSL(2,23)"Journal of Combinatorial Designs. 7. 147-155 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A.Bonnecaze,P.Gaborit,M.Harada,M.Kitazume,P.Sole: "Niemeier Lattices and Type II Codes over Z_4"Discrete Mathematics. 205. 1-21 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kitazume,M.Miyamoto,H.Yamada: "Ternary codes and vertex operator algebras"Journal of Algebra. 223. 379-395 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kitazume: "Some Non-split Extensions of the Orthogonal Group Ω(7,3)"Journal of Algebra. 224. 59-76 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Harada,M.Kitazume: "Z_4-Code Constructions for the Niemeier Lattices and Their Embeddings in the Leech Lattice"European Journal of Combinatorics. (発表予定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kitazume,K.Koike H.Shiga: "Notes on a certain integral orthogonal group and its quotient by the principal congruence subgroup of level 2"Kyusyu Journal of Mathematics. (発表予定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kitazume,M.Miyamoto,H.Yamada: "Borwein Identity and Vertex Operator Algebras"Journal of Number Theory. (発表予定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kitazume,C.H.Lam,H.Yamada: "Decomposition of the Moonshine vertex operator algebra as Virasoro modules"Journal of Algebra. (発表予定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M. Kitazume and A. Munemasa: "New 5-Designs with Auto-morphism Group PSL(2, 23)"Journal of Combinatorial Designs. 7. 147-155 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Bonnecaze, P. Gaborit, M. Harada, M. Kitazume and P. Sole: "Niemeier Lattices and Type II Codes over ZィイD24ィエD2"Discrete Mathematics. 205. 1-21 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Kitazume, M. Miyamoto and H. Yamada: "Ternary codes and vertex operator algebras"Journal of Algebra. 223. 379-395 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Kitazume: "Some Non-split Extensions of the Orthogonal Group Ω(7, 3)"Journal of Algebra. 224. 59-76 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Harada, M. Kitazume: "ZィイD24ィエD2-Code Constructions for the Niemeier Lattices and Their Embeddings in the Leech Lattice"European Journal of Combinatorics. (to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Kitazume, K. Koike and H. Shiga: "Notes on a certain integral orthogonal group and its quotient by the principal congruence subgroup of level 2"Kyushu Journal of Mathematics. (to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Kitazume, M. Miyamoto and H. Yamada: "Borwein Identity and Vertex Operator Algebras"Journal of Number Theory. (to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Kitazume, C. H. Lam and H. Yamada: "Decomposition of the Moonshine vertex operator algebra as Virasoro modules"Journal of Algebra. (to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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