1996 Fiscal Year Final Research Report Summary
Constructions of Matrix representations of Hecke algebras through W-graphs
| Project/Area Number |
08454019
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | NARA WOMEN'S UNIVERSITY |
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Principal Investigator |
OCHIAI Mitsuyuki Nara Women's University Department of Information and Computer Sciences Professor, 理学部, 教授 (70016179)
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| 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)
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| Project Period (FY) |
1996
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| Keywords | Knots / Matrix representations / Hecke Algebras / Invariants / Braids / W-graphs / Computer aided software / parallel invariants |
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| 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.
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