Categorification and KLR algebras

目的本项目将解决表示论前沿的三个问题：分次Hecke代数的中心猜想，晶体与KLR代数的具体联系，以及分次滤子Speht模的刻画。 重要意义解决这些问题中的任何一个都将代表着该领域的重大进步，并具有持久的影响和创造新的研究领域。 预期结果我们将消除理解KLR代数的主要瓶颈。 除了数学上的好处外，该项目所需并将得到加强的技能和专门知识很容易转让，并受到包括金融、信息技术和教育部门在内的工业界的追捧。

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.