| Project/Area Number |
19540012
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TERADA Itaru The University of Tokyo, 大学院・数理科学研究科, 准教授 (70180081)
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| Co-Investigator(Kenkyū-buntansha) |
小池 和彦 青山学院大学, 理工学部, 教授 (70146306)
田中 洋平 東京海洋大学, 海洋工学部, 教授 (00135295)
小林 俊行 東京大学, 大学院・数理科学研究科, 教授 (80201490)
岡田 聡一 名古屋大学, 大学院・多元数理科学研究科, 教授 (20224016)
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| Co-Investigator(Renkei-kenkyūsha) |
KOIKE Kazuhiko 青山学院大学, 社会情報学部, 教授 (70146306)
TANAKA Yohei 東京海洋大学, 海洋工学部, 教授 (00135295)
KOBAYASHI Toshiyuki 東京大学, 大学院・数理科学研究科, 教授 (80201490)
OKADA Soichi 名古屋大学, 大学院・多元数理, 教授 (20224016)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 組合せ論 / 全単射 / Robinson-Schensted対応 / Littlewood-Richardson規則 / Young図形 / ベキ零行列 / Jordan標準形 / 旗多様体 / ヤング図形 / ジョルダン標準形 / リトルウッド・リチャードソン則 / ロビンソン・シャンステッド対応 / シンプレクティック群 / 既約成分 / 代数多様体 / 対称群 / 冪等元 / デュアル・ペア / 冪零行列 / 半順序集合 |
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| Research Abstract |
Progress has been made in the efforts to obtain concrete understanding of the combinatorial bijections that had been tactfully constructed between Young tabueaux and generalizations, of which the Robinson-Schensted correspondence is a notable example, in relation with certain geometric objects appearing in representation theory, such as the variety of flags stable under a nilpotent matrix. A particular case was rapidly advanced with the help of viewpoints of other researchers. In addition, exchange with various researchers has brought several points to notice in the representations of classical groups and related objects as well as combinatorics, providing prospects of further developments in connection with previously experienced research topics.
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