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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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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 / Khovanov-Lauda-Rouqier代数 / 圏論化 / 標準加群 / Brauer-Humphreys相互律 / 量子群 / 偏屈層 / 大域基底 / 標準基底 / affine Hecke algebra / 局所Langlands対応 / 一般Springer対応 / 例外列 / quasi-hereditary代数 / exotic 冪零錐 / KLR代数 / exotic冪零錐 |
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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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Report
(4 results)
Research Products
(30 results)
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[Presentation] コストカ系と表現論2012
Author(s)
加藤周
Organizer
日本数学会2012年度年会,代数学分科会特別講演
Place of Presentation
東京理科大学
Year and Date
2012-03-26
Related Report
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