DFG-RSF: Geometry and representation theory at the interface of Lie algebras and quivers
DFG-RSF:李代数和箭袋接口的几何和表示论
基本信息
- 批准号:308831127
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Research Grants
- 财政年份:2016
- 资助国家:德国
- 起止时间:2015-12-31 至 2018-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The aim of the project is the study of various objects and structures endowed with large Lie groups of symmetries and linked to the geometric representation theory of quivers. The central innovative approach is to interleave the machinery of quiver representation theory and the methods and approaches of Lie theory in order to describe and study such objects, which are hard to deal with within one of the theories alone. The objects we are going to study include flag varieties and their degenerations, quiver Grassmannians, spherical and toric varieties, representations of finite and infinite-dimensional Lie algebras and their characters, and cyclic representations of abelian and contracted Lie algebras.The main objectives are:Description of toric degenerations of flag varieties and links with Newton-Okounkov theory, Study of the geometry of type A degenerate flag varieties and quiver Grassmannians, Description of PBW-type filtrations and associated graded spaces on highest weightrepresentations of simple and affine Kac-Moody Lie algebras, Development of a theory of quantum PBW filtrations, Description of algebro-geometric properties of finite and affine degenerate flag varieties, Study of the global geometry of the universal linear degeneration of type A flag varieties, Description of the structure of actions of Borel subalgebras and subgroups on naturalrepresentations and varieties, Description of graded characters of cyclic representations of current and affine algebras in terms of Macdonald polynomials.
该项目的目的是研究各种物体和结构,这些物体和结构被赋予了大的对称性李群,并与箭袋的几何表示理论有关。中心创新的方法是交错的机器的表征理论和方法和方法的李群理论,以描述和研究这样的对象,这是很难处理的一个理论单独。我们将要研究的对象包括旗簇及其退化、Grassmannian簇、球面簇和环面簇、有限维和无限维李代数的表示及其特征、交换李代数和压缩李代数的循环表示。主要目标是:描述旗形变种的复曲面退化并与牛顿-奥昆科夫理论联系,研究A型退化旗形变种和Grassmannian的几何形状,PBW型过滤和最高权重相关分次空间的描述简单和仿射Kac-Moody李代数的表示,量子PBW过滤理论的发展,有限和仿射退化标志簇的代数几何性质的描述,研究了A型旗簇的泛线性退化的全局几何,描述了Borel子代数和子群对自然表示和簇的作用结构,用Macdonald多项式描述了当前和仿射代数的循环表示的分次特征。
项目成果
期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Linear degenerations of flag varieties: partial flags, defining equations, and group actions
标志种类的线性退化:部分标志、定义方程和群动作
- DOI:10.1007/s00209-019-02451-1
- 发表时间:2019
- 期刊:
- 影响因子:0.8
- 作者:G. Cerulli Irelli;X. Fang;E. Feigin;G. Fourier;M. Reineke
- 通讯作者:M. Reineke
Linear degenerations of flag varieties
旗品种的线性退化
- DOI:10.1007/s00209-016-1839-y
- 发表时间:2017
- 期刊:
- 影响因子:0.8
- 作者:G. Cerulli Irelli;X. Fang;E. Feigin;G. Fourier;M. Reineke
- 通讯作者:M. Reineke
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Professor Dr. Markus Reineke其他文献
Professor Dr. Markus Reineke的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Professor Dr. Markus Reineke', 18)}}的其他基金
Quiver moduli and quantized Donaldson-Thomas type invariants
箭袋模量和量化 Donaldson-Thomas 型不变量
- 批准号:
219373365 - 财政年份:2012
- 资助金额:
-- - 项目类别:
Priority Programmes
Unitäre Darstellungen zwischen Physik und Mathematik bei George Mackey (1916 - 2006)
物理与数学之间的一神论表述,乔治·麦基 (George Mackey) (1916 - 2006)
- 批准号:
77330179 - 财政年份:2008
- 资助金额:
-- - 项目类别:
Research Grants
相似海外基金
DFG-RSF: Complex dynamical networks: effects of heterogeneity, adaptivity, and topology
DFG-RSF:复杂动态网络:异质性、适应性和拓扑的影响
- 批准号:
440145547 - 财政年份:2020
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Complex dynamical networks: effects of heterogeneity, adaptivity, and delays
DFG-RSF:复杂动态网络:异质性、适应性和延迟的影响
- 批准号:
308748074 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Dynamics of strongly non-equilibrium correlated systems at all time scales: dual representation of functional integral
DFG-RSF:所有时间尺度的强非平衡相关系统的动力学:函数积分的对偶表示
- 批准号:
310335100 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Doped-graphene for electrochemical energy storage and conversion: Impact of the electronic structure on electrocatalytic activity in oxygen redox reactions
DFG-RSF:用于电化学能量存储和转换的掺杂石墨烯:电子结构对氧氧化还原反应中电催化活性的影响
- 批准号:
310366325 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Impact of topology on electronic properties of ordered materials
DFG-RSF:拓扑对有序材料电子性能的影响
- 批准号:
310371528 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Towards a Molecular Source for Polarized Deuterium Fuel in NuclearFusion Research and other applications
DFG-RSF:在核聚变研究和其他应用中寻找极化氘燃料的分子源
- 批准号:
309228869 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Quantum interferometry with interacting electronic systems
DFG-RSF:交互电子系统的量子干涉测量
- 批准号:
310039433 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Beryllium based multilayer optics for the EUV spectral range
DFG-RSF:适用于 EUV 光谱范围的铍基多层光学器件
- 批准号:
310360704 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Nonequilibrium Phenomena and Interactions in Ultrapure III-V Nanowires
DFG-RSF:超纯 III-V 纳米线中的非平衡现象和相互作用
- 批准号:
310339015 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
DFG-RSF: Contribution of topological states to thermoelectric properties of Weyl semimetals
DFG-RSF:拓扑态对外尔半金属热电性能的贡献
- 批准号:
310375391 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants