K-theoretic Schubert Calculus for Grassmannians
| Project/Area Number |
16K17584
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | International Christian University (2020)
Okayama University of Science (2016-2019) |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | シューベルト多項式 / シュアー多項式 / グロタンディック多項式 / 旗多様体 / グラスマン多様体 / key多項式 / Lascoux多項式 / flagged Grothendieck多項式 / ラグランジアン・グラスマン多様体 / flagged tableaux / Q関数 / 同変コホモロジー / シューベルト類 / K理論 / Grothendieck多項式 / 行列式公式 / Bott-Samelson類 / algebraic cobordism / 代数的コボルディズム / タブロー公式 / Schur多項式 / シューベルト計算 |
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| Outline of Final Research Achievements |
The main result obtained from this research was the K-theoretic extensions of the proof of the determinant formula of type A Grassmannian Schubert classes by Kempf-Laksov and Damon and the Pfaffian formula of type C Lagrangian Grassmannian Schubert classes by Kazarian. As a consequence, we understand algebraic and combinatorial aspects of the Grothendieck polynomials. Based on this result, we will work on determining the Schubert coefficients for type C Grassmannians in future work.
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| Academic Significance and Societal Importance of the Research Achievements |
C型のシューベルトカルキュラスに関しては、シューベルト係数を求めるという問題は未解決の部分が多い。そんな中、シューベルト類の良い表示を代数的にも組み合わせ論的にも得られたことは、大きな進展であったと考える。
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Report
(6 results)
Research Products
(20 results)
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[Presentation] Tomoo Matsumura2019
Author(s)
A tableau formula of vexillary Schubert polynomials in type C
Organizer
The 46th Symposium on Transformation Groups
Related Report
Int'l Joint Research / Invited
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