2020 Fiscal Year Annual Research Report
The application of tau-tilting theory to Hecke algebras
| Project/Area Number |
20J10492
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| Research Institution | Osaka University |
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Principal Investigator |
王 起 大阪大学, 情報科学研究科, 特別研究員(DC2)
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| Project Period (FY) |
2020-04-24 – 2022-03-31
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| Keywords | Schur algebras / tau-tilting finite |
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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
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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| Strategy for Future Research Activity |
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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