1998 Fiscal Year Final Research Report Summary
RESEARCH ON THE MODULAR REPRESENTATIONS OF FINITE GROUPS
| Project/Area Number |
09640056
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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 | OSAKA CITY UNIVERSITY |
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Principal Investigator |
TSUSHIMA Yukio OSAKA CITY UNIV., FACULTY OF SCIENCE,PROF., 理学部, 教授 (80047240)
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| Co-Investigator(Kenkyū-buntansha) |
OKUYAMA Tetsurou HOKKAIDO UNIV.OF EDUCATION,PROFESSOR, 教授 (60128733)
YAMAGATA Kunio TOKYO UNIV.OF AGRICULTURE AND TECHNOLOGY,DEPARTMENT OF TECHNOLOGY,PROF., 工学部, 教授 (60015849)
KAWATA Shigeto OSAKA CITY UNIV., FACULTY OF SCIENCE,ASSOCIATE PROF., 理学部, 助教授 (50195103)
ASASHIBA Hideto OSAKA CITY UNIV., FACULTY OF SCIENCE,ASSOCIATE PROF., 理学部, 助教授 (70175165)
KANEDA Masaharu OSAKA CITY UNIV., FACULTY OF SCIENCE,PROF., 理学部, 教授 (60204575)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Broue conjecture / derived equivalence / perfect isometry / AR-sequence / Hecke algebra / symmetric group / groups of Lie type / D-module |
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| Research Abstract |
(1) Indecomposable modules over finite groups
Some contributions to the solution of the Broue conjecture are made especially in linear groups and the Glauberman correspondence cases. The tree classes of some Auslander-Reiten components for integral group rings of non cyclic p-groups are determined.
(2) Endomorphism rings of permutation modules
The orthgonality relation of characters of blocks of finite groups is generalized to that of blocks of Hecke algebras in the case where the base subgroup under consideration has order prime to the characteristic of the base field.
Some new results are obtained about the number of irreducible modular constituents of Specht modules of the symmetric group.
(3) Representation theory of groups of Lie type
Some foundations on the theory of D-modules in positive characteristic are established. A new approach is made using Kashiwara's crystal basis to Mathieu's theorem concerning the tensor products of modules with good filtrations.
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