| Project/Area Number |
20540006
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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 | Tokyo Institute of Technology (2011)
University of Tsukuba (2008-2010) |
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Principal Investigator |
NAITO Satoshi 東京工業大学, 大学院・理工学研究科, 教授 (60252160)
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| Co-Investigator(Kenkyū-buntansha) |
TAKEYAMA Yoshihiro 筑波大学, 数理物質系数学域, 准教授 (60375392)
SAGAKI Daisuke 筑波大学, 数理物質系数学域, 准教授 (40344866)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | リー環論 / 量子群の表現論 / アフィン量子群 / レベル・ゼロ表現 / Lakshmibai-Seshadri path / 結晶基底 / quantum Bruhat graph / 量子同変コホモロジー / Mirkovic-Vilonenサイクル / Mirkovic-Vilonen多面体 / Berenstein-Zelevinsky datum / アフィン・リー環 / 代数的サイクル / 量子群 / Demazure crystal / アフィン・グラスマン多様体 / Minkowski和 / 既約最高ウエイト加群 / Demazureクリスタル / Lakshmibai-Seshadriパス / 既約最高ウエイト表現 / 有限次元半単純り一環 |
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| Research Abstract |
In various areas of (mathematical) physics, such as particle physics, string theory, and statistical mechanics, affine Lie algebras appear as a natural symmetry; a quantum affine algebra is introduced as a q-deformations (or a quantum deformation) of the universal enveloping algebra of an affine Lie algebra.The study of representations (i.e., linear actions on vector spaces) of quantum affine algebras are very useful in examining the states of particles or strings.The main result of our research is an explicit combinatorial description, in terms of convex polytopes, of the crystal bases of Verma modules (i.e., the most universal highest weight modules) for type A quantum affine algebras.
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