2005 Fiscal Year Final Research Report Summary
Study of Classical and Quantum Integrable Systems and their discretizations
| Project/Area Number |
16540182
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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 | Tohoku University |
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Principal Investigator |
HASEGAWA Koji Tohoku University, Graduate School of Science, Lecturer, 大学院・理学研究科, 講師 (30208483)
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| Co-Investigator(Kenkyū-buntansha) |
KUROKI Gen Tohoku University, Graduate School of Science, Research Associate, 大学院・理学研究科, 助手 (10234593)
YAMADA Yasuhiko Kobe University, Faculty of Science, Professor, 理学部, 教授 (00202383)
IKEDA Takeshi Okayama Science University, Faculty of Science, Lecturer, 理学部, 講師 (40309539)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Integrable Systems / Affine Weyl groups / Painleve equation / Monodromy / Quantum groups |
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| Research Abstract |
K.Hasegawa studied the quantization of the discretized Painleve equation and its symmetries (Backlund transformations) proposed by K.Kajiwara, M.Noumi and Y.Yamada. Especially he succeeded to construct the quatization of the discrete Painleve VIth equation of Jimbo and Sakai.
G.Kuroki studied the quantization and discretization of the monodromy preserving deformation in general. He succeeded to reconstruct Hasegawa's quantization of Bcklund transformations from the viewpoint of dressing chains and geometric crystals. Also he tried to formulate the quantized theory as the deformation of the conformal field theory under the symmetry of W-algebras.
Y.Yamada studied the tropicalization of the structures relevant in the two dimensional solvable lattice statistical models, yielding many combinatorial corresspondances. Also studied are the discrete Painleve systems. Hypergeometric solutions for the elliptic and/or degenerate discrete Painleve equations are obtained. The method was applied to the Hamiltonian sturucture for the differential case.
T.Ikeda studied the reductions of solitonic equations. Heused the Fermionic Fock space to obtain a combinatorial formula for Schur's Q- functions. Also he succeded to identify Schur's Q-functions as some classes in equivariant cohomologies, suggesting that the study of special functions in the setting of torus action and its fixed points will be fruitful.
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Research Products
(10 results)
