2012 Fiscal Year Final Research Report
Crystal bases and their application to ultradiscrete integrable systems
| Project/Area Number |
21740114
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Keywords | アフィン量子群 / 可積分系 / 代数的組み合わせ論 / 艤装配位 / 結晶基底 / 箱玉系 |
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| Research Abstract |
When we try to understand the nature of an infinite dimensional algebra, one possible way is to find a natural basis which reflectsdeep properties of the algebra. Such a research sometimes brings an unexpected connection with another model in mathematical physics. In the case of the crystal bases of the quantum affine algebra the corresponding model is a typical example of the ultra-discrete soliton models called the box-ball system. The set of the action and angle variables of the box-ball systems, called the rigged configurations, serves as a natural basis which has a nice property even if we consider such deep property like the symmetry of the algebra of the symmetry.
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[Presentation] A survey on the box-ball systems2012
Author(s)
R. Sakamoto
Organizer
A Workshop on Algebraic Combinatorics related to Young diagrams and Statistical Physics
Place of Presentation
International Institute for Advanced Study, Kyoto
Year and Date
2012-08-06
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