2011 Fiscal Year Final Research Report
Realization of the crystal bases of level-zero representations of quantum affine algebras as algebraic cycles
| 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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| Keywords | リー環論 / 量子群の表現論 |
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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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