Algebraic Combinatorics of Symmetric Functions and its Applications to Representation Theory and Enumerative Combinatorics
| Project/Area Number |
18K03208
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Nagoya University |
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Principal Investigator |
Okada Soichi 名古屋大学, 多元数理科学研究科, 教授 (20224016)
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| Co-Investigator(Kenkyū-buntansha) |
石川 雅雄 岡山大学, 自然科学研究科, 教授 (40243373)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 対称関数 / 平面分割 / SchurのQ関数 / 中間斜交指標 / d-comoplete半順序集合 / rowmotion / 組合せ論 / 表現論 / 可積分系 / 半順序集合 / 凸多面体 |
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| Outline of Final Research Achievements |
We study several aspects of symmetric function theory toward applications to combinatorics, representation theory and integrable systems. 1. We present several identities and positivety conjectures for Schur Q-functions associated to the root system of type C. 2. We find a Weyl-type character formula for intermediate symplectic characters and give an application to the enumeration of certain plane partitions. 3. We give affine Gordon-Bender-Knuth identities for cylindric Schur functions and apply them to the combinatorics of cylindric standard tableaux.
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| Academic Significance and Societal Importance of the Research Achievements |
C型ルート系に付随したSchurのQ関数について，A型の場合と同様な関係式，正値性（予想）を見出した．これらの結果から背後に豊かな表現論的構造があることが期待され，新たな組合せ論，表現論を展開できる対象を提示できたとことに大きな意義がある．また，一連の研究においてパフィアンの絡んだ一般的な公式をいくつか与えることができ，幅広い分野に応用可能な手法を提供できた．
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Report
(6 results)
Research Products
(48 results)
