Invariant theory of theta-representations

theta 表示的不变理论

• 批准号: 219342514
• 负责人: Professorin Dr. Oksana Yakimova
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/219342514?language=en
• 关键词: Invariant; theory; theta; representations

One of the main tasks of mathematics is to describe certain objects up to a certain equivalence relation. Often this relation is given by an algebraic group action. Then the equivalence classes are the orbits and orbits closures correspond to degenerations of our objects. Thus, describing orbits of algebraic actions, as well as deciding whether one orbit lies in the closure of another, is an important and interesting problem. However, this is possible only in a very few cases. One of this instances is provided by the theta-representations introduced by E.B.Vinberg in the 70-s. The aim of this project is to study theta-representations and related objects, get a better understanding of their orbit structure, symmetric invariants, find out whether orbits closures have such nice properties as normality or rationality of singularities.

数学的主要任务之一是将某些对象描述成某种等价关系。这种关系通常由代数群作用给出。那么等价类就是轨道，轨道闭包对应于我们对象的退化。因此，描述代数作用的轨道，以及决定一个轨道是否在另一个轨道的闭包中，是一个重要而有趣的问题。然而，这只在极少数情况下是可能的。其中一个例子是E.B.Vinberg在70年代提出的theta-representation。本项目的目的是研究theta-表示及其相关对象，更好地理解它们的轨道结构、对称不变量，找出轨道闭包是否具有奇点的正态性或合理性等良好性质。