| Project/Area Number |
10640041
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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 | SCIENCE UNIV.OF TOKYO |
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Principal Investigator |
SHOJI Toshiaki Science Univ.of Tokyo, Fac of Science and Tech.Professor, 理工学部, 教授 (40120191)
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| Co-Investigator(Kenkyū-buntansha) |
HAMAHATA Yoshinori Science Univ.of Tokyo Fac.of Science and Tech.Lecturer, 理工学部, 講師 (90260645)
HOSOH Toshio Science Univ.of Tokyo Fac.of Science and Tech.Lecturer, 理工学部, 講師 (30130339)
AGOH Takashi Science Univ.of Tokyo Fac.of Science and Tech.Professor, 理工学部, 教授 (60112893)
ARIKI Susumu Tokyo Univ.of Mercantile Marine, Assoc.Prof., 商船学部, 助教授 (40212641)
SHINODA Ken-ichi Sophia Univ.Fac.of Science and Tech.Professor, 理工学部, 教授 (20053712)
大森 英樹 東京理科大学, 理工学部, 教授 (20087018)
田中 隆一 東京理科大学, 理工学部, 講師 (10112898)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1998: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | finite Cheralley group / Complex reflection group / representation theory / Ariki-Koike algebras / Hecke / Green / Hall-Littlewood / Schur-Weyl reciprocity / 複数鏡映群 / Frobenius formula / 代数群の表現論 / Kazhdan-Luszfig basis / canonical basis / 長さ関数 / 巡回Hecke環 / Character table / 指標層 |
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| Research Abstract |
I.We studied complex raflection group G(r, 1, n) and associated cyclotomic Hecke algebras (Ariki-Koike algebra). Inparticular, by making use of the Schur-Weyl reciprocity proved in the paper (Sakamoto-Shoji), we introdued new generators and relations for Ariki-Koike algebras. This enable use to show the Frobenius formula for the characters of Ariki-koike algebras, which was only known for the case of type Au.
II.Green function of type Au was introduced by Green in the study of representation theory of Ghn (Hg), and a combinatorial construction for it in terms of Schur-functions and Hall-Littlewood functions. Green fuctions for reductive groups in gewue was introduced by Deligne-Lusztig by using l-adis cohomology theory. In this research, we could extend the combinatorial approach as in the case of Au to the case of classical groups. Furthermore, our approach makes sense even is the case when weyl group is replaced by coplex reflection group G(r, 1, n).
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