2012 Fiscal Year Final Research Report
Global level set structure of ultradiscrete integrable systems
| Project/Area Number |
22540241
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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 | 防衛大学校 |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Keywords | 可積分系 / セルオートマトン / 量子群 |
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| Research Abstract |
We found and proved a new mathematical formula in the field of combinatorics. That is called a fermionic formula for partition functions associated with level set of a periodic integrable cellular automaton. By inventing a cellular-automaton-like description in terms of two colored strips, we also succeeded to construct a family of commuting phase flows (generalized time evolutions) in tropical periodic Toda lattice, a special discrete limit of well known Toda lattice in the field of classical integrable systems. The phase flows are important to determine the structure of the phase space of this dynamical system.
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