Applications of Representations of Quivers

箭袋表示法的应用

• 批准号: 0070658
• 负责人: Jerzy Weyman
• 金额: --
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070658&HistoricalAwards=false
• 关键词: Applications; Representations; Quivers

Abstract.This proposal is concerned with interactions between the representations of quivers, geometry and representation theory.The investigator will study the rings of semi-invariants of quivers and the combinatorial invariants they define. Special attention will be paid to the cone of weights of such rings and its relation to representation theory. In the special case of triple flag quivers this amounts to studying the cone defined by Klyachko inequalities. The principal investigator will also study the generalized quivers associated to reductive groups and their semi-invariants as well as the products of homogeneous spaces with finitely many orbits.Quivers are just oriented graphs. Their representations provide a convenient coding scheme allowing to study classification of objects arising in various areas of mathematics. The classification of matrices by their ranks and Jordan classificaton of endomorphisms of a vector space are the simplest examples. The more complicated ones include representations of classical groups and their generalizations to infinite dimensional algebras. Studying such classification problems, and conditions under which they can be explicitly solved is central in mathematical research. The investigator and his collaborators found that new interesting results can be obtained by using methods of invariant theory which were neglected before.

摘要：这个建议是关于箭图的表示，几何和表示理论之间的相互作用。研究者将研究箭图的半不变量环和它们定义的组合不变量。特别注意将支付给锥的重量等环和它的关系表示论。 在特殊情况下的三重旗颤抖这相当于研究锥定义的Klyachko不等式。 主要研究者还将研究与约化群及其半不变量相关的广义箭图，以及具有多个轨道的齐次空间的乘积。箭图只是定向图。 它们的表示提供了一种方便的编码方案，允许研究各个数学领域中出现的对象的分类。 矩阵的秩分类和向量空间的自同态的Jordan分类是最简单的例子。 更复杂的包括经典群的表示和它们对无限维代数的推广。 研究这样的分类问题，以及它们可以明确解决的条件是数学研究的核心。 研究者和他的合作者发现，通过使用以前被忽视的不变理论方法可以获得新的有趣结果。