| Project/Area Number |
24540032
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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 | Okayama University of Science |
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Principal Investigator |
IKEDA Takeshi 岡山理科大学, 理学部, 教授 (40309539)
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| Co-Investigator(Renkei-kenkyūsha) |
NARUSE Hiroshi 山梨大学, 教育人間科学部, 教授 (20172596)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
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| Keywords | 旗多様体 / K理論 / シューベルト類 / Littlewood-Richardson 規則 / シンプレクティック・グラスマン多様体 / Schubert 類 / 同変K理論 |
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| Outline of Final Research Achievements |
We studied the Schubert classes in the equivariant K-theory of generalized flag varieties G/P. First aim is to find good polynomial representatives for the Schubert basis. Second aim is to study the multiplicative structure constants of the Schubert basis by using the obtained polynomials.
We introduced the K-theoretic factorial P- and Q-functions which have several expressions both closed and combinatorial, and represent the Schubert basis of the maximal isotropic Grassmannians. Based on this result, we are able to formulate a conjecture for the structure constants for the maximal orthogonal Grassmannians in K-theory. By using the same underlying idea, we obtained a short proof of Littlewood-Richardson rule in K-theory. We also proved a Pfaffian sum formula for the symplectic Grassmannian in equivariant cohomology, and extended it to equivariant K-theory by using geometric technique. We also obtained a result for the equivariant quantum cohomology of maximal isotropic Grassmannians.
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