2022 Fiscal Year Final Research Report
Studies on integral representations of GKZ hypergeometric functions
| Project/Area Number |
19K14554
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Kumamoto University (2022)
Kobe University (2019-2021) |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | GKZ超幾何系 / 交叉理論 / twisted cohomology / 接続問題 / Feynman積分 |
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| Outline of Final Research Achievements |
In this project, we study integral representations of the so-called GKZ hypergeometric functions. The goal is to understand its global analysis. Moreover, we also seek applications of GKZ systems to sciences.
As a result, we described a formula of analytic continuation in terms of the secondary fan. We also clarified the combinatorial nature of an invariant that integral representations have ((co)homology intersection number). Moreover, we have developed applications for Feynman integrals in quantum field theory.
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| Free Research Field |
代数解析，特殊函数
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| Academic Significance and Societal Importance of the Research Achievements |
函数の性質を理解するうえで，その函数の満たす線形偏微分方程式系を理解することは重要である．しかし，勝手なホロノミー系を考えては具体的な解析は不可能である．GKZ超幾何系は，線形偏微分方程式系の中で大域的な解析が可能と期待される有力なクラスであるとともに，一般論では捨象されている組み合わせ的構造をもつ魅力的な対象である．本研究により，GKZ系の解析接続，積分表示に関する一般論が進展した．また，これらの成果は場の量子論の研究者からも興味を持たれ，共同研究へと繋がった．
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