Quantum Groups and Categorification in Geometric Representation Theory

几何表示理论中的量子群和分类

• 批准号: DE150101161
• 负责人: A/Prof Oded Yacobi
• 金额: $ 22.77万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-01-01 至 2018-03-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE150101161
• 关键词: Quantum; Groups; Categorification; Geometric; Representation

Representation theory, the mathematical study of symmetry, has applications in diverse areas such as particle physics, computer science, and molecular biology. This project aims to use a new family of quantum groups to prove a network of conjectures about categorical and geometric representation theory. The project aims to answer a long-standing open question in geometric representation theory concerning two families of geometric spaces underlying the theory of Lie groups. Representation theory is a strength of Australian mathematics, and this project aims to undertake pressing research at the forefront of this dynamic field.

表象理论是对对称性的数学研究，在粒子物理、计算机科学和分子生物学等不同领域都有应用。这个项目的目的是使用一个新的量子群族来证明一个关于范畴和几何表示理论的猜想网络。该项目旨在回答几何表示理论中一个长期悬而未决的问题，该问题涉及李群理论背后的两个几何空间族。表示理论是澳大利亚数学的强项，该项目旨在这一动态领域的前沿进行紧迫的研究。