Categorification and KLR algebras

分类和 KLR 代数

• 批准号: DP240101809
• 负责人: Prof Andrew Mathas
• 金额: $ 36.5万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-03-18 至 2026-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP240101809
• 关键词: Categorification; KLR; algebras

AIMS This project will solve three problems at the forefront of representation theory: the centre conjecture for graded Hecke algebras, concretely connecting crystals with KLR algebras and describing the grading and radical filtrations Specht modules. SIGNIFICANCE Solving any of these problems will represent a serious advance in the field and have a lasting impact and creating new areas of research. EXPECTED OUTCOMES We will remove major bottlenecks in our understanding of KLR algebras. BENEFITS In addition to the mathematical benefits, the skills and expertise that are required for, and will be enhanced by, this project are readily transferable and highly sought after by industry, including the financial, IT and education sectors.

本项目将解决表征理论前沿的三个问题：分级Hecke代数的中心猜想，晶体与KLR代数的具体连接，描述分级和自由基过滤光谱模块。