| Project/Area Number |
18K03223
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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 | Sophia University |
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Principal Investigator |
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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 |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | Schur多重ゼータ関数 / Pieri法則 / Shuffle積表示 / 双対公式 / 大野関係式 / ルート系ゼータ関数 / 対称多重ゼータ関数 / 多重ゼータ関数 / Pieri規則 / Shuffle積 / 双対性 / 大野関数 / ルート系のゼータ関数 / 多重対数級数 / Factorial Schur多項式 / Schur型多重ベルヌーイ数 / Schur関数 |
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| Outline of Final Research Achievements |
As combinatorial aspects of Schur multiple zeta functions, we obtained Pieri type formula and Shuffle product formula. As for the number theory aspects, (3) the dual formula and (4) its generalization called Ohno relation were obtained. Furthermore, we defined the Ohno function that determines the Schur-type Ohno relation, and succeeded in its complex interpolation. In addition, as an applied aspect, we have clarified the relationship with the zeta function of root system, contributed to the prediction of the relational expression between the Weyl group multiple zeta functions, and have extended it to functions with similar structures to symmetric functions including the Schur function..
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| Academic Significance and Societal Importance of the Research Achievements |
本研究成果は，Schur関数と類似の構造をもつ多重ゼータ関数が，Schur関数と同じ規則がなりたつこと，および多重ゼータ関数の性質の拡張が可能であることを示したことである．Schur関数は表現論および組合せ論における主要な研究対象であり，ゼータ関数やその多変数化である多重ゼータ関数は整数論における重要な研究対象である．これらの2つの研究分野について直接的な関係性は未解決であるが，本研究により研究手法の相互利用が可能であるということが示唆でき，大変有意義な成果が得られたと言える．
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