2011 Fiscal Year Final Research Report
Modular representation theory of algebras associated with complex reflection groups
| Project/Area Number |
22840025
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Shinshu University (2011)
Kyoto University (2010) |
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Principal Investigator |
WADA Kentaro 信州大学, 理学部, 助教 (60583862)
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| Project Period (FY) |
2010 – 2011
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| Keywords | 表現論 / Hecke代数 / Schur代数 / 複素鏡映群 |
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| Research Abstract |
We studied about modular representation theory of cyclotomic Hecke algebras and cyclotomic q-Schur algebras associated with the complex reflection groups of type G(r, 1, n). In the modular representation theory, it is one of the important problems to determine the character of modules. We described the character of Weyl modules of cyclotomic q-Schur algebras by using some combinatorics. We also defined induction and restriction functors. By using these functors, we showed that module categories of cyclotomic q-Schur algebras categorify the Fock space.
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