| Project/Area Number |
63460005
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Kyoto University |
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Principal Investigator |
KASHIWARA Masaki Kyoto University. Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (60027381)
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| Co-Investigator(Kenkyū-buntansha) |
NAKANISHI Noboru Kyoto University. Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (30027362)
TAKASAKI Kanehisa Kyoto University. Research Institute for Mathematical Sciences, Instructor, 数理解析研究所, 助手 (40171433)
SAITO Morihiko Kyoto University. Research Institute for Mathematical Sciences, Instructor, 数理解析研究所, 助手 (10186968)
MIWA Tetsuji Kyoto University. Research Institute for Mathematical Sciences, Associate Profes, 数理解析研究所, 助教授 (10027386)
KAWAI Takahiro Kyoto University. Research Institute of Mathematical Sciences, Professor, 数理解析研究所, 教授 (20027379)
島川 和久 京都大学, 数理解析研究所, 助手 (70109081)
荒木 不二洋 京都大学, 数理解析研究所, 教授 (20027361)
斎藤 恭司 京都大学, 数理解析研究所, 教授 (20012445)
大沢 健夫 京都大学, 数理解析研究所, 助教授 (30115802)
島田 信夫 京都大学, 数理解析研究所, 教授 (70027358)
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| Project Period (FY) |
1988 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥5,200,000)
Fiscal Year 1990: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1989: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1988: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | Kac-Moody algebra / Quantum group / Solvable lattice model / R matrix / Chiral Potts model / Hodge theory / unnarmonic oscillator / quantum gravity / 量子重力 / 無限次元多様体 / 結晶基底 / 共形場の理論 / 混合ホッジ加群 / 代数解析学 / 無限次元グラスマン多様体 / 無限次元リー環 / 共変量子力学 |
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| Research Abstract |
Kashiwara proved the generalized Kazhdan-Lustzig conjecture for Kac-Moody Lie algebras. He also proved the existence of special basis with certain nice properties at q=0 for representations of quantum groups. He named it crystal base and developed the theory. Miwa showed that crystal base is equivalent to the paths appearing in the computation of 1 point function of solvable lattice models, and, by using this fact, constructed the crystal base for the affine Lie algebras of type A. He also studied the representation theory of quantum when q is a root of unity and the related lattice models in the collaboration with Jimbo, Date, Miki. When q is a root of unity, quantum groups have a large center. The representations are classified by the values of these central elements. The R matrices exist only if they are chosen appropriately and Riimann surfaces appear form this condition. The corresponding lattice models, Which are the generalized chiral potts models, Were constructed. Morihiko Saito formulated the mixed Hodge modules as characteristic 0 analogue of the mixed Hodge theory of Deligne et al. Kawai studied the WKB method in connection with the unharmonic oscillators with Aoki and Takei, and obtained the canonical form of Schrodinger equation in the case of 1 or 2 simple turning points. Takasaki also studied the WKB method connecting Olver's method and the method of Jost solution in the scattering theory, and obtained multiple integral series for the Voros coefficients. Nakanishi studied the covariant canonical quantization of quantum gravity with Abe. They succeeded to obtain a consistent 1 order perturbation in Einstein gravitational constant, Without using a c-number background metric.
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