Towards further development of the representation theory of cyclotomic Hecke algebras

迈向分圆赫克代数表示论的进一步发展

• 批准号: 20340004
• 负责人: ARIKI Susumu
• 金额: $ 6.91万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20340004/
• 关键词: 表現論; ヘッケ代数; 準遺伝被覆; 圏化; 高階シューア代数; 巡回ヘッケ代数; モジュラー分岐則; Khovanov-Lauda代数

We have studied the representation theory of Hecke algebras, certain finite dimensional algebras which play important roles in Lie theory. Fock spaces originally appeared in mathematical physics and the categorification of the Fock spaces is an active field of research in recent days. We have also obtained several results which contribute to the development. The results obtained in the research include, identification of geometric and algebraic constructions of irreducible modules over the affine Hecke algebra of type A, theory to compute graded decomposition numbers of a graded quantized Schur algebra via categorification of the deformed Fock space, etc.

我们研究了Hecke代数的表示理论，这类有限维代数在李理论中起着重要的作用。Fock空间最初出现在数学物理中，Fock空间的分类是近年来一个活跃的研究领域。我们还获得了几项有助于发展的成果。得到的结果包括：A型仿射Hecke代数上不可约模的几何和代数构造的确定，分次量化Schur代数的分次分解数的计算理论等。

项目成果

Finite dimensional Hecke algebras

有限维赫克代数

• 发表时间: 2008
• 期刊: EMS series of Congress reports 2
• 作者: S.Ariki;N.Jacon;Susumu Ariki;横谷祐輔・田部絢子・石川衣紀・高橋智;磯部由香・早川巳貴・平島円;Susumu Ariki;Susumu Ariki
• 通讯作者: Susumu Ariki

Victor Kreiman, Shunsuke Tsuchioka, On the tensor product of two basic representations of U_v(\hat{sl}_e)

Victor Kreiman，Shunsuke Tsuchioka，关于 U_v(hat{sl}_e) 的两个基本表示的张量积

• 发表时间: 2008
• 期刊: Adv.Math. 218巻
• 作者: S.Ariki;N.Jacon;Susumu Ariki;横谷祐輔・田部絢子・石川衣紀・高橋智;磯部由香・早川巳貴・平島円;Susumu Ariki
• 通讯作者: Susumu Ariki

Introduction to KLR algebras

KLR 代数简介

• 发表时间: 2010
• 作者: S.Ariki;C.Lecouvey;N.Jacon;田部絢子・高橋智;堀光代 ・平島円・磯部由香・長野宏子;有木進
• 通讯作者: 有木進

Modular branching rule for the affine Hecke algebra of type A

A 型仿射 Hecke 代数的模分支规则

• 发表时间: 2010
• 作者: 高橋智;生方歩未;Susumu Ariki;高橋智・田部絢子;有木進
• 通讯作者: 有木進

Factorization of the canonical bases for higher-level Fock spaces

• DOI: 10.1017/s0013091510000519
• 发表时间: 2009-09
• 期刊: Proceedings of the Edinburgh Mathematical Society
• 影响因子: 0.7
• 作者: S. Ariki;N. Jacon;C. Lecouvey