Unified viewpoint for hypergeometric functions and the pentagonal number theorem based on representation theory
| Project/Area Number |
23654050
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
UMEDA Toru 京都大学, 理学(系)研究科(研究院), 准教授 (00176728)
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| Co-Investigator(Renkei-kenkyūsha) |
NOUMI Masatoshi 神戸大学, 自然科学系先端融合研究環重点研究部, 教授 (80164672)
ITOH Minoru 鹿児島大学, 大学院・理工学研究科, 准教授 (60381141)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 超幾何函数 / 五角数定理 / 表現論 / 不変式論 / q-analogue / 超幾何級数 |
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| Research Abstract |
The famous pentagonal number theorem by Euler has been extended as the description of the anomaly, that is, the difference of the trace of two matrices of infinite size, which are almost conjugate. Notable examples, among them, are inversion formulas for q-hypergeometric series. We investigate the mechanism behind that phenomena from the invariant-theoretic and representation-theoretic points of view, so that some new horizon for the hypergeometric series is opened. Dual pair theory is the key to withdraw the symmetry, even if it is not apparent.
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Report
(4 results)
Research Products
(33 results)
