2010 Fiscal Year Final Research Report
Representation Theory of Quantum Groups and Integrable Systems
| Project/Area Number |
20540016
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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 |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
OKADO Masato Osaka University, 大学院・基礎工学研究科, 准教授 (70221843)
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| Co-Investigator(Kenkyū-buntansha) |
NOBE Atsushi 千葉大学, 教育学部, 准教授 (80397728)
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| Research Collaborator |
SAKAMOTO Reiho 東京理科大学, 理学部, 助教 (30528055)
NAKASHIMA Toshiki 上智大学, 理工学部, 教授 (60243193)
FOURIER Ghislain Universitat zu Koln, Assistant
LECOUVER Cedric Universite Francois Rabelais, Professor
MISRA Kailash C. North Carolina State University, Professor
SCHILLING Anne University of California, Davis, Professor
SHIMOZONO Mark Virginia Tech, Professor
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| Project Period (FY) |
2008 – 2010
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| Keywords | 可積分系 / 量子群 / ヤン・バクスター方程式 |
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| Research Abstract |
We proved the existence of the crystal bases in the sense of Kashiwara for KR modules of the quantum groups of nonexceptional affine type, and determined their crystal structure. We then settled affirmatively the conjecture on the perfectness of KR crystals. By examining the combinatorial structure of the KR crystal, we solved the X=K conjecture by Shimozono-Zabrocki. On the other hand, we showed that a similar relation holds for the generating functions of rigged configurations, thereby solving the X=M conjecture for all nonexceptional affine types when the rank is sufficiently large.
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