Geometric Study of Quantum groups and Hecke algebras

量子群和赫克代数的几何研究

• 批准号: 23740014
• 负责人: KATO Syu
• 金额: $ 2.75万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740014/
• 关键词: 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 /

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).

代表理论Hecke代数和KLR代数在许多方面都很重要。我发现并证明了它们拥有许多标准模块的家族，其特性在准主代代数理论中对此有所回忆。 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规范/全球基础和PBW基地（lusztig的猜想）。

项目成果

An algebraic study of extension algebras

• DOI: 10.1353/ajm.2017.0015
• 发表时间: 2012-07
• 期刊: American Journal of Mathematics
• 影响因子: 1.7
• 作者: Syu Kato

On standard modules of affine Hecke algebras of classical types

经典型仿射赫克代数的标准模

• 发表时间: 2011
• 作者: 加藤周;加藤周;加藤周;加藤周;加藤周;加藤周;加藤周;Hiraku Kawanoue and Kenji Matsuki;加藤周
• 通讯作者: 加藤周

Exotic冪零錐と古典型 affine Hecke環の表現論

奇异的零幂圆锥与Hecke代数的经典型仿射表示论

• 发表时间: 2013
• 期刊: 数学
• 作者: Toshiyuki Abe;Yusuke Arike;Yusuke Arike;有家雄介;Yusuke Arike;有家雄介;有家雄介;有家雄介;有家雄介;加藤周;Syu Kato;加藤周
• 通讯作者: 加藤周

Kostka systems and its applications

Kostka系统及其应用

• 发表时间: 2013
• 作者: Dan Ciubotaru;Midori Kato;and Syu Kato;Satoshi Takagi;加藤周
• 通讯作者: 加藤周

On standard modules of affine Hecke algebras of classicaltypes

关于经典型仿射赫克代数的标准模

• 发表时间: 2011
• 作者: 加藤周;加藤周;加藤周;加藤周;加藤周;加藤周;加藤周
• 通讯作者: 加藤周