2014 Fiscal Year Final Research Report
Construction of tropical R maps on geometric crystals and its applications to crystal bases
| Project/Area Number |
22540031
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
TSUZUKI Masao 上智大学, 理工学部, 准教授 (80296946)
GOMI Yasushi 上智大学, 理工学部, 准教授 (50276515)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Keywords | 幾何結晶 / 結晶基底 / トロピカルR行列 / 多面体表示 / 一般化小行列式 / 単項式表示 / Bruhat cell / ワイル群 |
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| Outline of Final Research Achievements |
We considered decorated geometric crystals, which are deeply related to tropical
R-maps on geometric crystals.For types A,B,C,D and G, we obtained several results on the relations with monomial realizations of crystal bases.In particular, decoration functions of decorated geometric crystals are expressed as a sum of monomials with positive coefficients via generalized minors, which means that there exist certain interesting relations between monomial realizations and polyhedral realizations of crystal bases and these results are all new.
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| Free Research Field |
量子群、結晶基底、幾何結晶
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