Research on Lie theory and representation theory of algebras

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04782
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• 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): 2015-04-01 – 2018-03-31
• Keywords: ヘッケ代数 / 表現型

Outline of Final Research Achievements

Hecke algebras are finite dimensional algebras which occupy an important position in Lie theory. Nowadays they are generalized to wider class of cyclotomic quiver Hecke algebras. In this research, we have studied the cyclotomic quiver Hecke algebras for affine type C aiming at contruction of Specht modules, in view of the fact that Specht modules play an important role in the representation theory of the cyclotomic Hecke algebras of affine type A. The research is successful and the results are in the preprint arXiv:1703.06425. Furthermore, assuming that the base field is algebraically closed of odd characteristic, we have not only determined the representation type of block algebras of Hecke algebras of classical type but also have dtermined the algebra structure of those of finite representation type. The reults are published as a refereed paper in a journal.

Free Research Field

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