Modular representations of algebraic groups
| Project/Area Number |
23540023
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 |
KANEDA masaharu 大阪市立大学, 大学院・理学研究科, 教授 (60204575)
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| Co-Investigator(Renkei-kenkyūsha) |
TANISAKI Toshiyuki 大阪市立大学, 大学院理学研究科, 教授 (70142916)
YAGITA Nobuaki 茨城大学, 教育学部, 教授 (20130768)
TEZUKA Michishige 琉球大学, 理学部, 教授 (20197784)
FURUSAWA Masaaki 大阪市立大学, 大学院理学研究科, 教授 (50294525)
HASHIMOTO Yoshitake 東京都市大学, 知識工学部, 教授 (20271182)
KAWATA Shigeto 大阪市立大学, 大学院理学研究科, 准教授 (50195103)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 代数群 / modular表現 / Frobenius kernel / 量子群 / flag variety / cohomology / 代数群のmodular表現 / quadrics / G_1P-Verma modules / exceptional collection / reducitve group / parabolic induction / graded induction / Loewy series / rigidity / 国際研究者交流 仏蘭西 / Frobenius splitting / G_1T-Verma modules / 国際研究者交流 Australia / 国際情報交流 Denmark / G_1T-modules |
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| Outline of Final Research Achievements |
Let G be a reductive algebraic group over an algebraically closed field of positive characteristic p, P a parabolic subgroup of G, and T a maximal torus of P,
G_1 the Frobenius kernel of G. In joint work with Abe Noriyuki we determined the G_1T-structure of G_1P-Verma modules of p-regular highest weights for large p.
In joint work with H.H. Andersen we determined the cohomology vanishing behavior of line bundles on G/B in type G_2 when the corresponding B-modules lie in the lowest p^2-alcoves. In join work with M. Gros we constructed a Frobenius splitting on a quantum group at a root of unity.
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Report
(5 results)
Research Products
(14 results)
