| Project/Area Number |
16K17563
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tokyo University of Agriculture and Technology |
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Principal Investigator |
Naoi Katsuyuki 東京農工大学, 工学(系)研究科(研究院), 准教授 (40647898)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 量子アフィン代数 / Kirillov-Reshetikhin加群 / 結晶基底 / 古典極限 |
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| Outline of Final Research Achievements |
We have studied the classical limit of the tensor product of Kirillov-Reshetikhin modules, which is an important family of finite-dimensional simple modules over a quantum affine algebra, and it turned out that the module is constructed as the fusion product of the classical limits of the tensor factors.
In addition, it has been conjectured for a long time that Kirillov-Reshetikhin modules have crystal bases. We gave a proof to this conjecture in types G_2(1) and D_4(3), and for the special family called near adjoint.
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| Academic Significance and Societal Importance of the Research Achievements |
量子アフィン代数の有限次元既約加群のテンソル積の古典極限が, テンソル因子の古典極限のテンソル積と一致しないことは古くから知られていたが, その加群に関する研究はほとんど行われていなかった。今回の研究では非常に重要なKirillov-Reshetikhin加群の場合に, この方向性で新たな興味深い研究結果が得られた。その意義は高いと考えている。
またKirillov-Reshetkhin加群が結晶基底を持つ, という古くからある重要な予想を, 様々な場合に証明できたことも, 意義は高いと考えている。
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