2014 Fiscal Year Final Research Report
Understanding of the relation between degenerate hypergeometric functions and the matrix coefficients of the discrete series representations of semi simple Lie groups
| Project/Area Number |
23540005
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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 | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | 半単純リー群 / 超幾何関数 / 行列係数 / 離散系列 |
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| Outline of Final Research Achievements |
The special unitary group SU(3,1) of index (3,1) which is real rank 1 has so called the large discrete series representation as well as the (anti-)holomorphic ones. The matrix coefficients of the holomorphics are well known. In this study,
we obtained the radial part of the matrix coefficients of the large discrete series at the minimal K types using generalized hypergeometric functions. We also revealed that these are actually a combination of logarithm function and the rational functions with binomial coefficients by way of degeneracy of parameters.
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| Free Research Field |
整数論
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