Graded Hecke algebras and quasihereditary covers

分级赫克代数和准遗传覆盖

• 批准号: 23340006
• 负责人: ARIKI SUSUMU
• 金额: $ 5.32万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23340006/
• 关键词: 圏化; 箙ヘッケ代数; 表現型; 準遺伝被覆; 次数付ヘッケ代数; 準遺伝的被覆

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.

我们研究了分级赫克代数的表示论，称为箭袋赫克代数。引入箭袋赫克代数的目的是对量子群上的可积模进行分类。在研究的早期阶段，我们证明了某些非负性结果，这是我们谈论福克空间分类时所必须具备的性质。在该阶段之后，我们专注于仿射型量子群上基本模块的分类。很长一段时间我们只能处理仿射 A 型。在目前的研究中，我们已经成功地处理了仿射A型以外的其他仿射类型，并且证明了有限箭袋Hecke代数的Erdmann-Nakano型定理。特别是，它使我们能够详细分析驯服表示类型的有限箭袋赫克代数。与此分析相关，我们对两个点对称特殊双列代数进行了分类。

项目成果

Homomorphisms between neighboring G1T-Verma modules, Algebraic groups and quantum groups

相邻 G1T-Verma 模块、代数群和量子群之间的同态

• 发表时间: 2012
• 期刊: Contemp. Math
• 作者: H. Andersen;M. Kaneda;H. Nakajima;M. Kaneda
• 通讯作者: M. Kaneda

Constructing a q.h. cover of a cellular algebra

构建一个q.h。

• 发表时间: 2012
• 作者: S. Ariki;E. Park;Tomoki Nakanishi;S. Ariki;Tomoki Nakanishi;S. Ariki
• 通讯作者: S. Ariki

Representation type of finite quiver Hecke algebras of type D^{(2)}_{l+1}

D^{(2)}_{l 1} 型有限箭袋 Hecke 代数的表示类型

• 期刊: Trans. Amer. Math. Soc
• 作者: S. Ariki;E. Park
• 通讯作者: E. Park

Representation type of finite quiver Hecke algebras of type A^(2)_{2l}

A^(2)_{2l} 型有限箭袋 Hecke 代数的表示类型

• DOI: 10.1016/j.jalgebra.2013.09.005
• 发表时间: 2014
• 期刊: J. Algebra
• 作者: Susumu Ariki;Euiyong Park
• 通讯作者: Euiyong Park

Representation type of quiver Hecke algebras of type $A^{(2)}_{2\ell}$

$A^{(2)}_{2ell}$ 类型的箭袋赫克代数的表示类型

• 作者: Atsuo Kuniba;Masato Okado and Sergey Sergeev;Susumu Ariki;Hiraku Nakajima;有木進;Atsuo Kuniba and Masato Okado;Hiraku Nakajima;Susumu Ariki;Atsuo Kuniba and Shouya Maruyama;Susumu Ariki
• 通讯作者: Susumu Ariki