2015 Fiscal Year Final Research Report
Study of special functions which are captured by parametric deformations of representation-theoretical structures
| Project/Area Number |
25400044
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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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| 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) |
2013-04-01 – 2016-03-31
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| Keywords | 非可換調和振動子 / スペクトルゼータ関数 / アルファ行列式 / リース行列式 / 帯球関数 / ラテン方陣 |
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| Outline of Final Research Achievements |
We have studied a parametric deformation of the determinant and the quantum harmonic oscillator, which are equipped with nice invariance and symmetries.
As for the parametric deformation of the determinant, we have utilized relative invariants defined by such a deformation to introduce and study a generalization of the group determinants, to give a formula for the value of zonal spherical functions and irreducible characters for symmetric groups, and to prove the Alon-Tarsi conjecture on Latin squares in special cases.
As for the parametric deformation of the quantum harmonic oscillator, we have studied the functions which arise from a certain special value of the associated spectral zeta function which satisfies transformation rules similar to those for modular forms.
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| Free Research Field |
数物系科学
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