| Project/Area Number |
18K03212
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Osaka University |
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Principal Investigator |
ARIKI SUSUMU 大阪大学, 情報科学研究科, 教授 (40212641)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | ヘッケ代数 / 順表現型 / 多項式増大順表現型 / タウ傾理論 / 暴表現型 / シューア加群 / Hecke algebra / tau-tilting finite / 古典型ヘッケ代数 / Schur positive多項式 / 柏原クリスタル / tame block / Kashiwara crystal / Tokuyama formula |
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| Outline of Final Research Achievements |
In the previous research project 2015-2017, I determined Morita classes of blocks of Hecke algebras of classical type which are representation-finite. In the proof, classification of symmetric cellular algebras of finite representation type played an important role. Thus, it is natural to consider classification of symmetric cellular algebras of tame representation type. We have succeeded in classifying those which are tame of polynomial growth. After that, I have utilized tilting mutation to obtain the classification of Morita classes of tame blocks of Hecke algebras of classical type under the assumption that the characteristic of the base algebraically closed field is not equal to two.
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| Academic Significance and Societal Importance of the Research Achievements |
現代代数学において種々の体上の簡約群の表現論は保形形式その他の広い分野に関係する中心的な研究課題のひとつである。簡約群の表現論をより簡単な代数の表現論に帰着して研究する試みは昔から行われてきたが、ヘッケ代数はその文脈でよく使われる基本的な代数である。近年は簡約代数群に対しても正標数の体上の表現論が研究され始めており、ヘッケ代数のモジュラー表現論を先行して開発しておくことは学術上極めて有意義であると思われる。
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