| 研究課題/領域番号 |
20J10492
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| 研究機関 | 大阪大学 |
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研究代表者 |
王 起 大阪大学, 情報科学研究科, 特別研究員(DC2)
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| 研究期間 (年度) |
2020-04-24 – 2022-03-31
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| キーワード | Schur algebras / tau-tilting finite |
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| 研究実績の概要 |
In this year, we obtained some results about the tau-tilting finiteness of block algebras of Hecke algebras of type A, the main method we use is to find a tau-tilting infinite quotient algebra of such a block algebra. In particular, we have found that the algebras presented by some simple quivers with arbitrary admissible ideal are tau-tilting infinite.
Also, we have got nice criteria for the tau-tilting finiteness of most classical Schur algebras which are closely connected to the representation theory of Hecke algebras. The main idea of this is inspired by the proof process for the study of Hecke algebras.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
3: やや遅れている
理由
There are some difficulties in the original plan. Even though we have got some examples of tau-tilting finite/infinite blocks, we still cannot construct the complete boundary between tau-tilting finite blocks and tau-tilting infinite blocks.
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| 今後の研究の推進方策 |
On the one hand, we plan to add some restrictions on block algebras of Hecke algebras to get some complete results. On the other hand, we hope that the research of classical Schur algebras is useful for finding more tau-tilting infinite block algebras of Hecke algebras.
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