Geometric study of quantum groups and associative algebras
| Project/Area Number |
24540008
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Saito Yoshihisa 東京大学, 数理(科)学研究科(研究院), 准教授 (20294522)
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| Co-Investigator(Renkei-kenkyūsha) |
NAITO Satoshi 東京工業大学, 理工学研究科, 教授 (60252160)
IYAMA Osamu 名古屋大学, 多元数理研究科, 教授 (70347532)
TANISAKI Toshiyuki 大阪市立大学, 理学研究科, 教授 (70142916)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 結晶基底 / 量子群 |
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| Outline of Final Research Achievements |
The main results of this research are the followings.
(1) Recently, Kamnitzer gave a new realization of crystal bases of the quantized enveloping algebras of finite types, by using the theory of Mirkovic-Vilinen polytopes which has originated in geometry of affine Grassmannian varieties. In this research, we constructed an analogue of these theories for affine quantized enveloping algebras.
(2) We studied characteristic varieties of intersection cohomology complexes of Schubert varieties in type A. More explicitly, by using the method of geometric realization of crystal cases, we determined the explicit forms of these varieties in low rank cases.
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Report
(5 results)
Research Products
(16 results)
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[Presentation] 楕円ルート系について2016
Author(s)
Yoshihisa Saito
Organizer
信州代数セミナー
Place of Presentation
信州大学
Year and Date
2016-02-18
Related Report
Invited
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[Presentation] On Elliptic Artin Groups2015
Author(s)
Yoshihisa Saito
Organizer
Shanghai Conference on Representation Theory
Place of Presentation
Tian He Hotel (Shanghai,China)
Year and Date
2015-12-11
Related Report
Int'l Joint Research / Invited
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