2013 Fiscal Year Final Research Report
Graded Hecke algebras and quasihereditary covers
| Project/Area Number |
23340006
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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 | Osaka University |
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Principal Investigator |
ARIKI SUSUMU 大阪大学, 情報科学研究科, 教授 (40212641)
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| Co-Investigator(Renkei-kenkyūsha) |
TANISAKI Toshiyuki 大阪市立大学, 理学研究科, 教授 (70142916)
KANEDA Masaharu 大阪市立大学, 理学研究科, 教授 (60204575)
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| Project Period (FY) |
2011-04-01 – 2014-03-31
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| Keywords | 圏化 / 箙ヘッケ代数 |
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| Research Abstract |
We studied representation theory of graded Hecke algebras which are called quiver Hecke algebras. The quiver Hecke algebras were introduced for the purpose of categorifying integrable modules over quantum groups. In the early stage of the research, we proved certain nonnegativity result which was a property necessary to hold when we speak of categorification of Fock spaces. After that stage, we focused on categorification of basic modules over quantum groups of affine type. We were only able to handle the affine type A for long time. In the current research, we have succeeded in handling other affine types than affine type A and we have proved Erdmann-Nakano type theorems for finite quiver Hecke algebras. In particular, it allowed us to analyze finite quiver Hecke algebras of tame representation type in detail. Related to this analysis, we have classified two point symmetric special biserial algebras.
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