2010 Fiscal Year Final Research Report
Construction and classification of systems of multi-variable commutative differential operators
| 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(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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| 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 |
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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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[Presentation] BC_n 型q 超幾何関数の三項間隣接関係式とその応用2010
Author(s)
伊藤雅彦
Organizer
日本数学会秋季総合分科会無限可積分系セッション, および研究集会「BC 系とAGT 予想の周辺」2010年9月11日, および神戸可積分系セミナー, および青山数理セミナー
Place of Presentation
名古屋大学, 東京大学, 神戸大学, 青山学院大学
Year and Date
20100421-20100925
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