Dualities in the representation theory and geometry of loop groups

环群表示论和几何的对偶性

• 批准号: 219517305
• 负责人: Professor Dr. Peter Fiebig
• 金额: --
• 依托单位: Department 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 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/219517305?language=en
• 关键词: Dualities; representation; theory; geometry; loop

Representation theory is the study of symmetries appearing in mathematics, physics or in any other natural science. Its main objective is to give an a priori description of data that can appear in a system that exhibits a given symmetry. For „classical" symmetries (finite groups, compact Lie groups, etc.) a large amount of such data is known today. In recent years various new classes of symmetries appeared in the context of infinite dimensional loop groups. Quite surprisingly, significant interrelations between these structures and other areas of mathematics were found. The recurrent appearance of “dualities” belongs to the deepest mysteries in today's mathematics. The project intends to study these dualities by combining two approaches towards the representation theory of loop groups and related structures such as modular or quantum representations.

表示论是研究出现在数学、物理学或任何其他自然科学中的对称性。它的主要目标是给出一个先验的描述数据，可以出现在一个系统，表现出给定的对称性。对于“经典”对称（有限群，紧李群等）目前已知大量这样的数据。近年来，在无限维循环群的背景下出现了各种新的对称类。令人惊讶的是，这些结构和数学的其他领域之间的重要的相互关系被发现。经常出现的“对偶性”属于最深的奥秘，在今天的数学。该项目旨在通过结合两种方法来研究这些对偶性，以实现循环群的表示理论和相关结构，如模块或量子表示。