Research on generalized cohomology of flag varieties and Schur functions and their variants
| Project/Area Number |
15K04876
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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 |
Geometry
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| Research Institution | Okayama University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
成瀬 弘 山梨大学, 大学院総合研究部, 教授 (20172596)
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| Co-Investigator(Renkei-kenkyūsha) |
IKEDA Takeshi 岡山理科大学, 理学部, 教授 (40309539)
NAKADA Kento 岡山大学, 教育学研究科, 准教授 (70532555)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | トポロジー / 旗多様体 / 一般コホモロジー / Schur関数 / Hall-Littlewood関数 / Gysin写像 / 複素コボルディズム / シューベルト・カルキュラス / 幾何 / Schur S, P, Q-関数 / P-コンパクト群 / Schur S-, P-, Q-関数 / Schubert calculus / 幾何学 / Schur S-, P, Q-関数 |
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| Outline of Final Research Achievements |
We studied a generalization of the Gysin formulas for the Hall-Littlewood polynomials due to Pragacz to the complex-oriented generalized cohomology theory. We introduced the universal Hall-Littlewood functions, and established the universal Gysin formulas for them. We also studied a generalization of the Darondeau-Pragacz formulas in the ordinary cohomology theory to the complex cobordism theory, and extended their formulas in the case of type A flag bundles. In the course of our study, we introduced the universal factorial Hall-Littlewood P- and Q-functions, and were able to obtain the generating functions for them as a by-product of our formulas.
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Report
(4 results)
Research Products
(8 results)
