2009 Fiscal Year Final Research Report
Construction of affine geometric crystals and Representation theory of crystal bases
| Project/Area Number |
19540050
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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 | Sophia University |
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Principal Investigator |
NAKASHIMA Toshiki Sophia University, 理工学部, 教授 (60243193)
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| Co-Investigator(Kenkyū-buntansha) |
SHINODA Kenーichi 上智大学, 理工学部, 教授 (20053712)
TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946)
GOMI Yasushi 上智大学, 理工学部, 講師 (50276515)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 結晶基底 / 幾何結晶 / 超離散化 / ヘッケ環 / 代数群 / Tropical R写像 / 保型形式 |
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| Research Abstract |
For most affine Kac-Moody algebras, we constructed geometric crystals associated with the simplest KR modules. We also obtained tropical R maps explicitly. Furthermore, only for sl (2)-case, certain universal type tropical R maps have been constructed. As a criterion for homogeneity of geometric crystals, we showed that the crystal obtained by the ultra-discretization is connected. By this criterion, it turns out that we can show easily the uniqueness of tropical R maps. We got epsilon systems of type A.
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