Combinatorics of partially ordered sets and quantum symmetries
Project/Area Number |
16K05083
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Meijo University |
Principal Investigator |
|
Project Period (FY) |
2016-04-01 – 2022-03-31
|
Project Status |
Completed (Fiscal Year 2021)
|
Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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)
|
Keywords | 代数的組合せ論 / 量子代数 / 鏡映群 / Hopf代数 / 代数学 / 半順序集合 |
Outline of Final Research Achievements |
The aim of the project is to study the structure of (finite) partially ordered sets from the viewpoints of combinatorial ring theory and of quantum deformations. One of the main results of this project is the Lefschetz property for a certain class of Gorenstein algebras associated with matroids. This result implies the Sperner property for the geometric modular lattices. I also introduced the notion of the Solomon-Terao algebra for hyperplane arrangements with the collaborators, and have shown its basic properties. The quantum K-theory for the flag variety was also studied in the project. The correspondence between quantum Grothendieck polynomials and K-k-Schur functions has been proved as a K-theoretic analogue of the Peterson isomorphism.
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Academic Significance and Societal Importance of the Research Achievements |
順序集合は理論的な考察対象としてのみならず、応用数理においても重要な役割を果たしている。本研究は、組合せ環論的アプローチや量子変形の観点から順序構造の組合せ的研究を目指したものである。 主な成果としてマトロイドから定まるGorenstein環を導入し、そのLefschetz性を研究したが、これは今後マトロイドに関わる組合せ環論の研究において基礎的な結果になるものと考えられる。 また、旗多様体の量子K環に関して量子Grothendieck多項式とK-k-Schur多項式との対応を研究したが、これはWeyl群上のBruhat順序の拡大とアフィンWeyl群上のBruhat順序の対応に相当している。
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Report
(7 results)
Research Products
(10 results)