1989 Fiscal Year Final Research Report Summary
| Project/Area Number |
01044073
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| Research Category |
Grant-in-Aid for Overseas Scientific Survey.
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| Allocation Type | Single-year Grants |
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| Research Institution | Research Institute for Mathematical Sciences, Kyoto University |
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Principal Investigator |
ARAKI Huzihiro Professor, Research Institute for Mathematical Sciences, Kyoto University, 数理解析研究所, 教授 (20027361)
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| Co-Investigator(Kenkyū-buntansha) |
JIMBO Michio Assoc. Prof., Faculty of Science, Kyoto University, 理学部, 助教授 (80109082)
MIWA Tetsuji Assoc. Prof., Research Institute for Mathematical Sciences, Kyoto University, 数理解析研究所, 助教授 (10027386)
MIZOHATA Sigeru Professor, Osaka Electro-Communication University, 教授 (20025216)
KASHIWARA Masaki Professor, Research Institute for Mathematical Sciences, Kyoto University, 数理解析研究所, 教授 (60027381)
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| Project Period (FY) |
1989
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| Keywords | Non-commutative analysis / Master symmetries / Q-analogue / Colored oriented graph / Tensor product / Kazhdan-Lusztig conjecture / Flag variety / Kac-Moody Lie algebra |
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| Research Abstract |
An inequality of Lieb and Thirring about the trace of product of powers of two non-commutative operators is generalized to a general power parameter values by H. Araki to provide a tool for non-commutative analysis. Master symmetries of one-dimensional XY-model in statistical mechanics of spin lattice systems are mathematically analyzed and their basic properties are proved by using operator algebraic methods by H. Araki as a typical example of a non-commutative analysis. A canonical basis for an irreducible representations of the q-analogue of a universal enveloping algebra for A_n, B_n, C_n and D_n cases is found and shown to have a structure of a colored oriented graph, with application to a combinatorial description of the decomposition of the tensor product into irreducible components, by M. Kashiwara. The generalization of Kazhdan-Lusztig conjecture for symmetrizable Kac-Moody Lie algebras is proved by H. Kashiwara by using an infinite dimensional flag variety.
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