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Constructions of Matrix representations of Hecke algebras through W-graphs

Research Project

Project/Area Number 08454019
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionNARA WOMEN'S UNIVERSITY

Principal Investigator

OCHIAI Mitsuyuki  Nara Women's University Department of Information and Computer Sciences Professor, 理学部, 教授 (70016179)

Co-Investigator(Kenkyū-buntansha) YAMASHITA Yasushi  Nara Women's University Department of Information and Computer Sciences Assistan, 理学部, 講師 (70239987)
KOBAYASHI Tsuyoshi  Nara Women's University Department of Information and Computer Sciences Professo, 理学部, 教授 (00186751)
WADA Masaaki  Nara Women's University Department of Information and Computer Sciences Associat, 理学部, 助教授 (80192821)
KAKO Fujio  Nara Women's University Department of Information and Computer Sciences Professo, 理学部, 教授 (90152610)
Project Period (FY) 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥6,100,000 (Direct Cost: ¥6,100,000)
Fiscal Year 1996: ¥6,100,000 (Direct Cost: ¥6,100,000)
KeywordsKnots / Matrix representations / Hecke Algebras / Invariants / Braids / W-graphs / Computer aided software / parallel invariants / ミュータント結び目
Research Abstract

The purpose of this research is to construct a software to assist researches about Knot Theory. It assists to compute all polynomial invariants and in particular, parallel polynomial invariants related with knots and links. We had constructed a computer software, Knot Theory by Computer which works on Windows 95 and Windows NT.The software has the following features :
(1)to construct knots and links by mouse tracking,
(2)to deform knots by mouse operations,
(3)to visualize knots and links by 3-dimensional computer graphics,
(4)to compute all polynomial invariants which have already known,
(5)to compute 3-parallel polynomial invariants associated with 3,4, and 5 braids
(6)to recognize to whether a knot to be trivial or not (but not complete),
This software will be distributed worldwide through leternet (ftp.ics.nara-wu.ac.jp) by the end of April, 1998. In future research, we will construct new features to compute 4-parallel polynomial invariants associated with 4-braids and establish a method to construct any irreducible representations associated with Hecke algebras. The well known Lascoux-Schutzenberger's method is correct by up to 13 of braid index but false greater than 13.

Report

(2 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] 落合・鴨・土井・今藤: "結び目と平面グラフの最適埋蔵" 情報処理学会・数理モデル化と問題解決・報告集. 10-5. 33-40 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Kobayashi, M.Kobayashi: "On Canonical genus and free genus of knots." J.of Knot theovy and its ramifications. 5. 77-85 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Kobayashi, D.Heath: "Essential tangle decomposition from thin position of a link." Pacific J.Math.179. 107-117 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Wada, Yamashita, Yoshida: "An inequality for poly-hedra and ideal triangulation of cusped hyperbolic3-manifolds." Proc. Amer.Math.Soc. 124. 3905-3911 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Wada: "Parabolic representation of the groups of mutant knots." J. of knot theory and its ramifications.6. 895-904 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 今藤・落合: "結び目理論研究支援ソフトウェアにおける自明な結び目判定アルゴリズム" 情報処理学会・数理モデル化と問題解決・報告集. 6. 1-6 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 落合・山田・豊田: "コンピュータによる結び目理論入門" 牧野書店, 193 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] OCHIAI,KAMO,DOI,AND IMAFUJI (in Japanese): "Nicely embeddings of knots and planar graphs" Information Processing Society of Japan, Mathematical Modelling and Problem Solving Report. 5. 33-40 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.KOBAYASHI AND M.KOBAYASHI: "On canonical genus and free genus of knots" J.of Knot theory and its ramifications. 5. 77-85 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.KOBAYASHI AND D.HEATH: "Essential tangle decomposition from thin position of a link" Pacific J.Math. 179. 107-117 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.WADA,Y.YAMASHITA,AND H.YOSHIDA: "An inequality for polyhedra and ideal triangulation of cusped hyperbolic 3-manifolds" Proc.A.M.S.124. 3905-3911 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.WADA: "Parabolic representation of thegroups of mutant knots" J.of Knot theory and its ramifications. 6. 895-904 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.IMAFUJI AND M.OCHIAI (in Japanese): "Computer aided Knot theory and an algorithm to Recognize whether a knot to be trivial" Information Processing Society of Japan, Mathematical Modelling and Problem Solving Report. 6. 1-6 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] OCHIAI,YAMADA,AND TOYODA (in Japanese): Introduction to Computational Knot Theory. Makino Shoten, 1-193 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 落合・鴨・土井・今藤: "結び目と平面グラフの最適埋蔵" 情報処理学会・数理モデル化と問題解決報告表. 10-5. 33-40 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Kobayashi、M.Kobayashi: "On canonical genus and free genus of Knot" J.of knot theory and its yamifications. 5. 77-85 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Kobayashi: "Examples of hyperbolic knot which do not admit depthl foliation" Kobe J.Math.15. 209-221 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Kobayashi D.Heath: "Essential tongle decomposition from thin position of a link" Pacific J.Math.(to appear).

    • Related Report
      1996 Annual Research Report
  • [Publications] Wada,Yamashita,Yoshida: "An inequality for polyhedra and icleal triusgulations of cusped hyperbolic 3-manl foids" Proc.Amer.Math.Soc.(to appear).

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Wada: "Parabolic representions of the groups of mutant knots" J.of knot theory and its rsmifieations. (to appear).

    • Related Report
      1996 Annual Research Report
  • [Publications] 落合豊行・山田修司・豊田英美子: "コンピュータによる結び目理論入門" 牧野出版, 193 (1996)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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