Graded semisimple deformations

表示理论的最新进展揭示了对称群和Hecke代数的经典表示理论中美丽的新结构。这些发现为我们提供了新的代数--割圆KLR代数，它们编码了代数组合学和几何表示理论中基本对象的深层性质。割圆箭图Hecke代数是数学中几个公开问题的核心，但人们对它们的了解仍然很少，甚至连它们的基本性质，如它们的维度都是未知的。这个项目将为研究这些代数建立一个新的框架，这将消除这一领域目前的障碍，并使我们能够证明实质性的新结果，促进理论的发展。

Recent advances in representation theory have revealed beautiful new structures in the classical representation theory of the symmetric groups and Hecke algebras. These discoveries have provided us with new algebras, the cyclotomic KLR algebras, that encode deep properties of fundamental objects in algebraic combinatorics and geometric representation theory. The cyclotomic quiver Hecke algebras are central to several open problems in mathematics but they are still poorly understood, with even basic properties like their dimensions being unknown. This project will establish a new framework for studying these algebras that will remove the current obstacles in this field and alllow us to prove substantial new results that advance the theory.