Research on finite dimensional algebras and combinatorial objects that appear in Lie theory

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K03212
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: Osaka University
• Principal Investigator: ARIKI SUSUMU 大阪大学, 情報科学研究科, 教授 (40212641)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: ヘッケ代数 / 順表現型 / 多項式増大順表現型

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.

Free Research Field

表現論

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。