2013 Fiscal Year Final Research Report
Representation theory of affine Hecke algebras and quanum groups via geometry, category and combinatorics
| Project/Area Number |
22740011
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Electro-Communications (2013)
Kyoto University (2010-2012) |
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Principal Investigator |
ENOMOTO Naoya 電気通信大学, 情報理工学(系)研究科, 准教授 (50565710)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 表現論 / 量子群 / ヘッケ環 / 結晶基底 / 大域基底 / LLTA理論 / 曲面の写像類群 / Johnson準同型 |
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| Research Abstract |
We mainly study the structure of Johnson cokernels for the mapping class group of surfaces via several representation theoretic approaches. The notion of Johnson cokernels gives an approximation of the mapping class group of surfaces using a certain graded Lie algebras. We have no series in the Johnson cokernels except for "the Morita obstruction" in 1990's.
In this research, we introduce a new class in Johnson cokernels for the automorphism groups of the free groups and the mapping class groups. Moreover, the class is combinatorially computable by using some representation theoretic method for the general linear groups and the symplectic groups. Moreover, we give a new series "anti-Morita obstructions" in the Johnson cokernels. This is a joint work with Takao Staoh.
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