| Project/Area Number |
19540226
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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 |
Global analysis
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| Research Institution | Aoyama Gakuin University |
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Principal Investigator |
TANIGUCHI Kenji Aoyama Gakuin University, 理工学部, 准教授 (20306492)
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| Co-Investigator(Kenkyū-buntansha) |
小池 和彦 青山学院大学, 理工学部, 教授 (70146306)
伊藤 雅彦 青山学院大学, 理工学部, 准教授 (30348461)
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| Co-Investigator(Renkei-kenkyūsha) |
KOIKE Kazuhiko 青山学院大学, 社会情報学部, 教授 (70146306)
ITO Masahiko 東京電機大学, 未来科学部, 准教授 (30348461)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 可換微分作用素 / Calogero模型 / Whittaker模型 / q-差分方程式 / q-超幾何関数 / Calogero 模型 / ジャクソン積分 |
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| Research Abstract |
We studied several topics related to the systems of commutative differential operators. Obtained results are as follows :
(1) The arrangement of singular lines of a pair of commutative differential operators of rank two with an inverse square potential function is determined by the stationary points of the potential function of BC-type Sutherland model.
(2) The explicit formula of the discrete series Whittaker functions on Spin(2n,2).
(3) The standard Whittaker (g,K)-modules are defined. Their structures are determined when (i) the infinitesimal character is generic, and (ii) the group is U(n,1) and the infinitesimal character is integral.
(4) Three-term relations between interpolation polynomials for a BC_n-type hypergeometric series.
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