Combinatorics of Schubert calculus and its application
| Project/Area Number |
25400041
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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 | University of Yamanashi (2015)
Okayama University (2013-2014) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
IKEDA Takeshi 岡山理科大学, 理工学部, 教授 (40309539)
NAKAGAWA Masaki 岡山大学, 教育学研究科, 准教授 (50370036)
ISHIKAWA Masao 琉球大学, 教育学部, 教授 (40243373)
HAGIWARA Manabu 千葉大学, 理学研究科, 准教授 (80415728)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | シューベルト・カルキュラス / 同変コホモロジー / 同変K理論 / 対称函数 / グラスマン多様体 / 一般コホモロジー / シューア函数 / 退化跡 / Casselman問題 / Schur函数 / Hall-Littlewood函数 / 同変K-理論 / hook公式 / 組合せ論 / シューア関数 |
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| Outline of Final Research Achievements |
We defined good polynomial representative of torus equivariant Schubert class in K-theory of flag varieties of the classical groups. We also give combinatorial formula for them. As an application of equivariant Schubert calculus we give a proof of the hook formula, which gives the number of standard tableaux on a given shape of partition. We also give a generalization of the hook formula and its equivariant K-theory version. By alanogy with this formula we get a solution to the Casselman's problem related to the representation of p-adic algebraic groups using some techinques of Schubert calculus.
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Report
(4 results)
Research Products
(11 results)
