2009 Fiscal Year Final Research Report
Algebraic Analysis of Infinite Symmetry
| Project/Area Number |
18340007
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyoto University |
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Principal Investigator |
KASHIWARA Masaki Kyoto University, 数理解析研究所, 教授 (60027381)
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| Co-Investigator(Kenkyū-buntansha) |
ARIKI Susumu 京都大学, 数理解析研究所, 准教授 (40212641)
KIRILLOV Anatol 京都大学, 数理解析研究所, 准教授 (30346035)
MIWA Tetsuji 京都大学, 大学院・理学研究科, 教授 (10027386)
NAKAJIMA Hiraku 京都大学, 数理解析研究所, 教授 (00201666)
NAITO Satoshi 筑波大学, 数理物質科学研究科, 准教授 (60252160)
KANEDA Masaharu 大阪市立大学, 大学院・理学研究科, 教授 (60204575)
TANISAKI Toshiyuki 大阪市立大学, 大学院・理学研究科, 教授 (70142916)
NAKASHIMA Toshiki 上智大学, 理工学部, 教授 (60243193)
NAKAYASHIKI Tasushi 九州大学, 大学院・数理額研究院, 准教授 (10237456)
SUZUKI Takeshi 岡山大学, 大学院・自然科学研究科, 准教授 (30335294)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 表現論 / 量子群 / 結晶基底 / 変形量子化 / アフィンヘッケ環 |
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| Research Abstract |
I have studied representation theory via geometric methods and categorical methods. I conjectured that the representation theory of affine Hecke algebras of type B is described by the symmetric crystals which we introduced for this purpose. I also studied deformation quantizations of the structure sheaf of symplectic manifolds, and applied this theory to the study of the representation theory of rational Cherednik algebrasvia a deformation quantization of the Hilbert scheme of surfaces. I also succeeded to express the K-theory of the flag manifolds of affine Lie algebras by the polynomial rings.
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