2001 Fiscal Year Final Research Report Summary
Crystal basis in quantum groups and its applications
| Project/Area Number |
12640385
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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 |
物理学一般
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KUNIBA Atsuo The University of Tokyo, Graduate School of Arts and Sciences Associate professor, 大学院・総合文化研究科, 助教授 (70211886)
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| Co-Investigator(Kenkyū-buntansha) |
OKADO Masato Osala University of Tokyo, Graduate School of Enginnering Science Associate professor, 大学院・基礎工学研究科, 助教授 (70221843)
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| Project Period (FY) |
2000 – 2001
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| Keywords | statistical mechanics / solvable lattice models / Yang-Baxter equation / quantum groups / affine Lie algebra / crystal basis / soliton cellular automaton / Bethe ansatz |
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| Research Abstract |
There are two main achievements in the two years. The first one is about the fermionic formula and related topics. We generalized the fermionic formula to all the twisted quantum affine algebras and gave a unified description on various aspects including the tensor product theorem in path realization, spinon character formulae, dilogarith sum rules, the Kirillov-Reshetikhin conjecture, completeness of Bethe ansatz both at q = 1 and q = 0 and so forth. Combinatorial R for all non exceptional algebras is also obtained in terms of an explicit insertion algorithm.
The second one is about the soliton cellular automata constructed from the crystal basis. We proved that the scattering rule of solitions is identical with the combinatoral R for smaller rank algebra. We proved in the infinite carrier case that the time evolution is factorized into a product of Weyl group operators. This greatly simplified the description of the dynamics into the motion of particles and antiparticles that undergo pair creation and annihilation. For An^<(1)> case, we constructed N-soliton solution by exploring the connection to the discrete KP equation.
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Research Products
(34 results)
