2005 Fiscal Year Final Research Report Summary
A Study on Derived Equivalences of Blocks and Shintani Descent in Group Algebras
| Project/Area Number |
16540001
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hokkaido University of Education |
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Principal Investigator |
OKUYAMA Tetsuro Hokkaido University of Education, Faculty of Education, Professor, 教育学部旭川校, 教授 (60128733)
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| Co-Investigator(Kenkyū-buntansha) |
HASEGAWA Izumi Hokkaido University of Education, Faculty of Education, Professor, 教育学部札幌校, 教授 (50002473)
KOMURO Naoto Hokkaido University of Education, Faculty of Education, Professor, 教育学部旭川校, 教授 (30195862)
YATSUI Tomoaki Hokkaido University of Education, Faculty of Education, Associate Professor, 教育学部旭川校, 助教授 (00261371)
KITAYAMA Masashi Hokkaido University of Education, Faculty of Education, Professor, 教育学部釧路校, 教授 (80169888)
IAI Shin-ichiro Hokkaido University of Education, Faculty of Education, Associate Professor, 教育学部札幌校, 助教授 (50333125)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Representations of Finite Groups / Block Algebras / Splendid Tilting Complexes / Shintani Descent / Broue's Conjecture |
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| Research Abstract |
In the research of this project, we studied "the abelian defect conjecture" which is one of main problems in representation theory of finite groups. We were concerned with Shintani descent and Glauberman correspondent.
1.We have constructed one sided tilting complexes for finite Chevalley groups of small rank, for example, U(3,q^2)、Sp(4,q)、G_2(q). We could construct Splendid tilting complexes which coincide with these complexes as one side complexes and studied perfect isometries between character rings induced by them.
2.The situations described in 1 can be considered problems of derived category version of "Glauberman correspondent". We have studied solvable group case and obtain some generalization of results by Harris and Linckelmann. And we clarify the strategy raised by Rouquier in this setting.
3.We also worked on a problem giving quiver presentations for various types of 5-Sylow normalizers of rank 2 to apply for constructing tilting complexes of some finite Chevalley groups, for example, ^2F_4(q) of which 5-Sylow normalizer is of 4S_4-type.
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Research Products
(11 results)
