Affine algebras, Lie superalgebras, Hecke algebras, and representations
仿射代数、李超代数、赫克代数和表示
基本信息
- 批准号:0800280
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2008
- 资助国家:美国
- 起止时间:2008-07-01 至 2011-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Wang's research proposal covers three very active areas of representation theory and aims to stretch them into new directions: (i) the Hecke algebras associated to double covers of the Weyl groups and their representations. He proposes to construct the quantum ``spin" Hecke algebras of finite, affine, and double affine types. Then he intends to develop the representation theory of these algebras at different levels of degeneration and connections to noncommutative geometry; (ii) modular representations of finite-dimensional (simple) Lie superalgebras over an algebraically closed field of prime characteristic. In particular, Wang proposes to establish a superalgebra analogue of the Kac-Weisfeiler conjecture and connections to finite W-superalgebras; and (iii) modular representation theory of affine Lie algebras over an algebraically closed field of prime characteristic. He proposes to study systematically Wakimoto modules, at the critical and non-critical levels, and affine W-algebras in the framework of modular vertex algebras.The mathematical language used to describe symmetries in nature and supersymmetry proposed by physicists often involves the concept of groups or algebras. Representation theory is a way of studying complicated groups and algebras by expressing them in matrix forms, sometimes in a deliberately simplified manner. One outcome of studying representations is to see how symmetries differ from one another and how seemingly different symmetries are related to each other. The study of groups and algebras has numerous applications to physics, chemistry, cryptography, and others. Wang's research will broaden the scope of the study of several central concepts in representation theory in the last three decades: Hecke algebras, Lie superalgebras, and affine Lie algebras.
Wang的研究计划涵盖了表示论的三个非常活跃的领域,并旨在将它们扩展到新的方向:(i)与Weyl群及其表示的双覆盖相关的Hecke代数。他建议构建量子"自旋”赫克代数有限,仿射,双仿射类型。然后,他打算发展的代表性理论,这些代数在不同层次的退化和连接到非交换几何;(ii)模块化表示有限维(简单)李超代数在代数封闭领域的主要特点。特别是,王建议建立一个超代数类似的卡茨-Weisfeiler猜想和连接有限W-超代数;和(iii)模表示理论的仿射李代数在一个代数闭域的主要特征。他提出在临界和非临界水平上系统地研究Wakimoto模,并在模顶点代数的框架下研究仿射W-代数。物理学家提出的用于描述自然界对称性和超对称性的数学语言经常涉及群或代数的概念。表示论是一种研究复杂群和代数的方法,通过矩阵形式来表达它们,有时以故意简化的方式。研究表征的一个结果是看到对称性如何彼此不同,以及看似不同的对称性如何彼此相关。群和代数的研究在物理学、化学、密码学和其他领域有许多应用。王的研究将拓宽在过去三十年中表示论的几个中心概念的研究范围:Hecke代数,李超代数和仿射李代数。
项目成果
期刊论文数量(0)
专著数量(0)
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会议论文数量(0)
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Weiqiang Wang其他文献
Braid group symmetries on quasi-split ıquantum groups via ıHall algebras
- DOI:
- 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
Weiqiang Wang - 通讯作者:
Weiqiang Wang
Quantum Schur Duality of Affine type C with Three Parameters
三参数仿射C型量子Schur对偶性
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:1
- 作者:
Zhaobing Fan;Chun-Ju Lai;Yiqiang Li;Li Luo;Weiqiang Wang;Hideya Watanabe - 通讯作者:
Hideya Watanabe
Fast exact fingerprint indexing based on Compact Binary Minutia Cylinder Codes
基于紧凑二进制细节柱码的快速精确指纹索引
- DOI:
10.1016/j.neucom.2017.10.027 - 发表时间:
2018-01 - 期刊:
- 影响因子:6
- 作者:
Chaochao Bai;Weiqiang Wang;Tong Zhao;Mingqiang Li - 通讯作者:
Mingqiang Li
Investigation on characteristics of tensile damage and microstructure evolution of steel AISI 316L by nonlinear ultrasonic Lamb wave
非线性超声兰姆波研究AISI 316L钢拉伸损伤特征及微观组织演化
- DOI:
10.1016/j.ijpvp.2022.104680 - 发表时间:
2022 - 期刊:
- 影响因子:3
- 作者:
Jianxun Li;Minghang Wang;Haofeng Chen;Pengfei Wang;Weiqiang Wang - 通讯作者:
Weiqiang Wang
Hecke-Clifford Algebras and Spin Hecke Algebras I: The Classical Affine Type
Hecke-Clifford 代数和自旋 Hecke 代数 I:经典仿射类型
- DOI:
- 发表时间:
2007 - 期刊:
- 影响因子:0
- 作者:
T A Khongsap;Weiqiang Wang - 通讯作者:
Weiqiang Wang
Weiqiang Wang的其他文献
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{{ truncateString('Weiqiang Wang', 18)}}的其他基金
Quantum Groups, W-algebras, and Brauer-Kauffmann Categories
量子群、W 代数和布劳尔-考夫曼范畴
- 批准号:
2401351 - 财政年份:2024
- 资助金额:
-- - 项目类别:
Standard Grant
Quantum Symmetric Pairs, Categorification, and Geometry
量子对称对、分类和几何
- 批准号:
2001351 - 财政年份:2020
- 资助金额:
-- - 项目类别:
Continuing Grant
Canonical Bases, Categorification, and Modular Representations
规范基础、分类和模块化表示
- 批准号:
1702254 - 财政年份:2017
- 资助金额:
-- - 项目类别:
Continuing Grant
Representation theory and quantum symmetric pairs
表示论和量子对称对
- 批准号:
1405131 - 财政年份:2014
- 资助金额:
-- - 项目类别:
Standard Grant
Representations of Lie superalgebras, Hecke algebras and affine algebras
李超代数、赫克代数和仿射代数的表示
- 批准号:
1101268 - 财政年份:2011
- 资助金额:
-- - 项目类别:
Standard Grant
Conference on Nonassociative Algebra in Action: Past, Present, and Future Perspectives
行动中的非结合代数会议:过去、现在和未来的观点
- 批准号:
1106203 - 财政年份:2011
- 资助金额:
-- - 项目类别:
Standard Grant
Summer school and conference on geometric representation theory and extended affine Lie algebras
几何表示理论和扩展仿射李代数暑期学校和会议
- 批准号:
0903278 - 财政年份:2009
- 资助金额:
-- - 项目类别:
Standard Grant
Duality between representations of Lie superalgebras and Lie algebras via Kazhdan-Lusztig theory
通过 Kazhdan-Lusztig 理论研究李超代数和李代数表示之间的对偶性
- 批准号:
0500374 - 财政年份:2005
- 资助金额:
-- - 项目类别:
Standard Grant
Conference on Infinite-Dimensional Aspects of Representation Theory and Applications; Charlottesville, VA; May 2004
表示理论与应用的无限维方面会议;
- 批准号:
0401095 - 财政年份:2004
- 资助金额:
-- - 项目类别:
Standard Grant
Representations of Infinite Dimensional Lie Algebras and the McKay Correspondence
无限维李代数的表示和麦凯对应
- 批准号:
0196434 - 财政年份:2001
- 资助金额:
-- - 项目类别:
Standard Grant
相似国自然基金
数学物理中精确可解模型的代数方法
- 批准号:11771015
- 批准年份:2017
- 资助金额:48.0 万元
- 项目类别:面上项目
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局部扩展仿射李代数的结构、分类和表示论
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仿射李代数表示论与复曲面和三重滑轮的枚举几何
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567867-2022 - 财政年份:2022
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EP/N023919/1 - 财政年份:2016
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扭曲仿射李代数的平铺
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497351-2016 - 财政年份:2016
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Relation between representations at the critical level and those of level zero for affine Lie algebras and semi-infinite flag manifolds
仿射李代数和半无限标志流形的临界层表示与零层表示之间的关系
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