2010 Fiscal Year Final Research Report
Towards further development of the representation theory of cyclotomic Hecke algebras
| Project/Area Number |
20340004
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyoto University |
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Principal Investigator |
ARIKI Susumu Kyoto University, 大学院・情報科学研究科, 教授 (40212641)
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| Co-Investigator(Renkei-kenkyūsha) |
KATO Syu 京都大学, 大学院・理学研究科, 准教授 (40456760)
TANISAKI Toshiyuki 大阪市立大学, 大学院・理学研究科, 教授 (70142916)
SHOJI Toshiaki 名古屋大学, 大学院・多元数理科学研究科, 教授 (40120191)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 表現論 |
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| Research Abstract |
We have studied the representation theory of Hecke algebras, certain finite dimensional algebras which play important roles in Lie theory. Fock spaces originally appeared in mathematical physics and the categorification of the Fock spaces is an active field of research in recent days. We have also obtained several results which contribute to the development. The results obtained in the research include, identification of geometric and algebraic constructions of irreducible modules over the affine Hecke algebra of type A, theory to compute graded decomposition numbers of a graded quantized Schur algebra via categorification of the deformed Fock space, etc.
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