2013 Fiscal Year Final Research Report
Geometric Study of Quantum groups and Hecke algebras
| Project/Area Number |
23740014
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
KATO Syu 京都大学, 理学(系)研究科(研究院), 准教授 (40456760)
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| Project Period (FY) |
2011 – 2013
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| Keywords | アフィンヘッケ環 / スプリンガー対応 / 形式次数 / 冪零錐 / 局所ラングランズ対応 / 同変導来圏 / 幾何学的拡大環 / コストカ系 |
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| Research Abstract |
Representation theory of affine Hecke algebras and KLR algebras are important in many aspect. I find and proved that they possess many families of standard modules whose properties are reminicent to these in the theory of quasi-hereditary algebras. In particular, they satisfies the some kind of ``orthogonality property". Such an orthogonality property (and some ordering on irreducible representations) determines the characters, and seems to capture the orthogonality of characters in more primitive fashion.
As applications, we proved the finiteness of the global dimension of KLR algebras (a question raised by Kashiwara), and the positivity of the transition matrix between canonical/global bases and PBW bases (a conjecture of Lusztig).
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