Study of special functions which arise from parametric deformations ofrepresentation-theoretical structures
| Project/Area Number |
22540028
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of the Ryukyus |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 非可換調和振動子 / スペクトルゼータ関数 / 特殊値 / α行列式 / 既約分解 / 帯球関数 / 表現論 / 特殊関数 |
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| Research Abstract |
We have studied a parametric deformation of the determinant and the quantumharmonic oscillator, which are equipped with nice invariance and symmetries. As for the parametric deformation of the determinant, we found certain family of symmetric polynomials by using such deformationsfor special parameters. As for the parametric deformation of the quantum harmonic oscillator, we showedthat the function which describes a certain special value of the associated spectral zeta function satisfiestransformation rules similar to those for modular forms.
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Report
(4 results)
Research Products
(26 results)
